since the first reply by schrdinger to the famous epr paper the word `` entanglement '' has been primarly used for indicating a class of quantum states that shows non local features . discussing the dynamical properties of a composite system made of two subsystems that , after mutual interaction , move away one from the other einstein podolsy and rosen concluded that quantum mechanics was not - complete and that some more local ( hidden ) dynamical variables would have been necessary for a correct description of the physical reality .essentially , they pointed to two quantum mechanical aspects that they found counter intuitive . in primis , the possible ambiguity of the wave function so that ``  as a consequence of two different measurements performed upon the first system , the second system may be left in states with two different wave functions  '' .the second aspect was later indicated , by einstein itself , as a _ spooky action at distance _ `` since at the time of measurement the two systems no longer interact , no real change can take place in the second system in consequence of anything that may be done to the first system  '' .we nowadays know that they were wrong and that quantum mechanics gives , so far , a complete representation of this strange phenomenon .  up to the late fifties of last centurythe debate on entanglement was mostly confined to the fundamental aspect of quantum mechanics and the word itself had nt any particular operational meaning . in 1957 a paper by bohm and aharonov moved the focus from the original _ gedankenexperiment _ toward more feasible and intuitive physical implementations and , in particular , to spin like systems .this paved the way to a more complete theoretical analysis of the hidden variables scenario that leads to the famous bell inequalities for dichotomic quantum variables .this made spin like systems the preferential candidates for proving the failure of any hidden variables hyphotesis .single photons have been then widely used in several experimental tests of the bell inequalities ( see for a review ref .very recently , a novel experiment made the photon the first physical system for which each of the main loopholes has been closed .on the other hand , the original formulation of the epr paradox was based on continuous variable systems .so that , in 1986 reid and walls proposed the first translation of bell inequalities into the continuous varaible language and in 1992 the first experimental realization of an epr like system appeared .since then , a few more attempts have been carried out for translating the bell argument into the language of continuous variables ( cv ) . among themthe one proposed by banaszek and wdkiewicz considers the relation between the wigner function of the state and non locality .entanglement , in its orignal formulation , states the existence of global states of a composite system which can not be written as a product of states of individual subsystems . while this definition set an univoque border between separable and entangled states, entanglement gives rise to different features of quantum systems and can be seen under different perspectives .on one hand , mathematically defining entanglement as a property of the composite system wavefunction , make it intrinsically related to pure states . on the other hand , we all know that experimentally acessible states are mixed , so that feasible entanglement tests have to be related to density matrices rather than wave functions werner1989.  in this paper we aim at discussing the operational meanings of different criteria usually employed for assessing cv entanglement .in particular , we will link each of them to different facets of the original entanglement debate .we will apply them to entangled gaussian states ( gs ) weedbrook2012,olivares2012 produced by a type ii sub threshold frequency degenerate opo . by experimentally analysing the properties of experimentally generated cv entangled states we will express all these criteria in terms of the covariance matrix elements .moreover , we give a novel handy relation that describes in a simple way the connection among entanglement , purity and bell s non - locality . the experimental analysisprove that some entanglement features are strongly hold against decoherence while bell inequality is violated only for nearly pure states .the paper is organized as follows . in sect .ii the properties of guassian states are reviewed .then , in sect .iii , a summary of different entanglement criteria is given .each of the presented criteria is related to a particular feature of entanglement . in sectiv a bell - type inequality is given in terms of the gaussian states properties . while in sect .v a discussion on the effects of decoherence on states violating bell inquality is presented . in sect .vi we report an overview on some experimental results and , in particular , an _ a posteriori _ bell test on an effective bipartite cv entangled state . eventually , in sect .vii conclusions are drawn .a continuous - variable bi partite gs is a two - mode state , on the hilbert space , whose characteristic function or , equivalently , wigner function in phase space is gaussian: } }  \label{wigner}\]]where is the vector of a set of orthogonal quadratures , for mode and respectively .( being ) .we remind that the pair and ( = i$ ] ) associated to a single _ e.m . _ mode is the analogue to the position / momentum pair for a mechanical oscillator .this makes optical mode a good candidate for replicating epr states in their original fashoin .all the features of gs are embedded in the second order momenta of the joint quadrature distribution , namely the covariance matrix ( cm ) in eq .( wigner ) .a pure gs can be seen as the action of a displacement and a squeezing operator onto the vacuum state . while , the most general mixed gs can be obtained replacing the vacuum with a thermal field at finite temperature .  for a bipartite statethe is a matrix , with elements ( being the anti commutator ) . can be written in the form and represent self correlation of the single subsystem and describes the cross correlation between the two subsystems .remarkably , a gs represents any quantum system whose evolution can be described by a at least bilinear bosonic hamiltonian . in particularthis is the case of optical parametric oscillators ( opo ) .any cm , representing a physical state , can be transformed into the so - called standard form  means of local symplectic transformations where , , and are determined by four local symplectic invariants , , , . as a matter of fact , a sub threshold type ii opo , due to the symmetry of its hamiltonian , can only produce states whose cm is a standard form . hereafter, whenever we refer to cms we will mean such standard form .moreover , at the time of birth inside the non linear crystal , the bipartite state we would analyse in the following shows and .  from the symplectic invariants it is possible to give a criteria for disitnguishing among physical and non - physical cms . describes a physical state iff we also note that a pure gs is a minimum uncertainty state and that the cm relative to a pure state necessary has so that for a pure state , for mixed symmetric states , . in general, for a bipatite gs , the purity reads } } .\label{gausspur}\ ] ]a quantitative measure of entanglement for a mixed state is , so far , an unsolved issue .this is probably due to the different operational implications that different levels of quantum correlation open . at the same time , there exist different necessary and/or sufficient conditions to asses whether a given state is entangled or not .these criteria are easily translated into experimental tests for entanglement . herewe aim to look at the different criteria and connect them , logically , to the debate on the original epr paper .the first criterion was developed by considering the definition of entangled states : a state of a composite system whose wavefunction can not be given as product of sub - systems wavefunction . or , in the case of mixed states , following the werner extension to the relative density matrix werner1989 .in the bi partite case a density matrix represent a separable state iff its can be written as a convex combination of the tensor product of density operators relative to the two sub systems while  are the density matrices of subsystems and .the criterion can be casted considering that if one performs a partial transposition ( _ i.e. _ transposition of the density matrix with respect to only one of the two hilbert subspaces ) transform into that , for a state written in form given in eq .( [ sepst ] ) will still represent a physical state of the composite system .conversely , if the state un separable , the tranformed density operator would have no more a physical counterpart .this criterion , is sometime referred to as the _ ppt _ criterion ( _ positivity _ under _ partial transposition _ ) or phs from the names of the people that proposed it for discrete ( peres and horodecki horodecki1997 ) and continuous variables ( simon ) .translated into the cm language a bi partite gaussian state is separable iff it is entangled otherwise .we also note that the phs criterion is invariant under symplectic transformations and that for pure states the inequality is saturated .  the phs criterion set , then , is roots into the fact that two systems that have interacted can not , even if the split apart after the interaction , be described independently .  a second crierion , the duan one , has been derived considering that in presence of an entangled state also the heisenberg uncertainty principle , written for the joint system and a pair of epr - like operators , has to take into account the inherent quantum correlation .the duan criterion , a necessary condition for entanglement , for a cm in the usual standard form reads: based on the calculation of the total variance of a pair of einstein- podolsky - rosen ( epr ) type operators .it relies on the fact that the inherent correlation reduces the total variance that , in separable states , is greater than the sum of the standard quantum limit applied to the single subsystem . in the case of frequencydegenerate type ii opo , this result in the squeezing of the modes obtained by letting the two entagled companions interfere .a stronger bound can be found by considering the original epr _ gedankenexperiment _ where the paradox was found in the possibility of determining the state of a far - away system by measuring its entangled companion .for this reason this criterion is usually indicated as the epr criterion and was firstly introduced by reid in 1989 , in the very early days of quantum information .it describes the ability to infer the expectation value of an observable on a sub system by performing a suitable measurement on the second sub system .this criterion sets only a sufficient condition for assessing entanglement being a stricter condition on the strenght of quantum correlation. it can be easily given in terms of cm elements : the criterion is asymmetric under the exchange of the two sub - systems so that the two definitions can make it ambiguous if one of the relations is not satisfied .this is not the case of balanced systems ( ) where this one - side violation is not possible .the asymmetry of the criterion allows to use it for the so called steering capability : the state of a far away system can be steered by a suitable measurement on its entangled companion handchen2012 .generally , if we want to evaluate the non - locality of a state through a chsh inequality , the operative form of the bell one , we should build a bell operator representing a combination of dichotomic ( true - false ) measurements . then, if the expectation value of such a bell operator violates the corresponding inequality , the system is not considered local , otherwise it would admit a classical description in terms of hidden variables .a parity operator is dichotomic .it can be constructed , on the photon number , for assigning or depending on whether an even or an odd number of photons has been registered . in refs .banaszek1998,banaszek1999prl a connection between the wigner function of the state and the joint measurement of the parity operator performed on the bi partite quantum state has been shown .  herewe want to give a handy expression that relates such a measurement to the cm of a generic gs .we consider the bell operator in the form given in eq .( 7 ) of ref .the bell type function then , given by the linear combination of four expectation values  the wigner function of the state calculated in and where are complex amplitudes ( and so is is eq .( [ bell ] ) ) .local theories , admitting a description in terms of local hiddden variables , set the bound  on one hand , any bell inequality concerns the analysis of joint probabilities measured at space time separated locations .so that , to actually perform a bell measure we should need to make repeated simultaneous measurements at different space time separated locations stochastically changing the detector settings ( in this case the amounts of displacement ) . then by statistical analysis we could conclude or not the violation of the chsh type inequality .  on the other hand , eq .( [ corr ] ) show that the knowledge of the wigner function , i.e. the full reconstruction of the quantum state gives an insight to the local / non local character of the state . without running into delicate questions we wish to show that , being a gs fully described by a rather simple object , the cm , it is possible to evaluate , _ a posteriori _ , on the state so to asses whether or not it is bell correlated without the need of reconstructing the whole wigner function .this paves the way to a handy experimental procedure to disciminate among different levels of quantum correlations .now , we consider the bipartite gs generated by a type ii opo described by the covariance matrix ( [ cm initial ] ) , with and .  it can be esaily found that the quantity ( [ bell ] ) becomes bell function depends on the state properties ( ) and on a free parameter ( ) . to look for the maximum violation for a given state we need to look for the value of the displacement amplitude that nullifies the derivative .the maximum is , then , obtained for\]]so that reads  \label{b}\]]this gives the expectation value of the maximum value of the bell operator as a function of the gaussian state parameters .so that , being possible to experimentally retrieve the cm of such a state prl2009 , this formula can be used to perform an _ a posteriori _test on the non local property of the state .moreover , it is possible to relate to the purity of the single subsystem . having in mind the interconnection between entanglement and the purity of the constituent sub systems , we have:  \label{bwc}\]]where the correlation coefficient whose limit for a pure state is   it can also be proved that , when the gaussian state is pure , can be considered an entanglement witness : any entangled state violates the bell inequality and viceversa .   for mixed states the above equivalence does not hold . given a mixed system , one has .so that , for a given correlation coefficient , it is possible to set three boundaries for the values of ^{1/2}\text { , }  \notag \\ \mu _ { p } & = & \left [ 1-c_{ab}^{2}\right ] ^{1/2}.\end{aligned}\]]so that denotes separable states , indicates entangled states that do not violate the bell inequality , and , finally , for the states are entangled and violate the bell inequality . for the relative cm would be not physical . in this way it is possible to distinguish three ( physical ) regions in the plane ( see fig .[ bvscmus ] )  * region * : :  separable states compatible with the local hidden variables theory  ( ) .* region * : :  entangled states compatible with the local hidden variables theory  ( ) .* region * : :  entangled states not compatible with the local hidden variables theory  ( ) .  it is clear that there are nt separable gs that violate the bell s inequality . instead , a state compatible with a local theory ( _ i.e. _ compatible with a theory in hidden variables ) can also be entangled .this confirms the existence of different forms of quantum correlations and non locality .   as function of purity and the correlation coefficient . for the different meanings of the plor regionssee text.,scaledwidth=45.0% ]in this section we want to analyze the behaviour of the bell s nonlocality subjected to passive gaussian noise .we will see that when a pure ( ) , entangled and bell s non local ( i.e. ) state evolves through a gaussian channel , retains its entanglement , but looses its bell s nonlocality .this means that although , at the time of its birth , the state is pure , so that it violates bell s inequality and breaks the duan bound , decoherence highlights the different nature of the two markers : the gaussian state becomes local ( in according to bell ) , i.e. it would admit a description in terms of local hidden variables , although it remains entangled .  a bipartite state , described by the eq . ( [ cm initial ] ) , subjected to the action of a passive gaussian channel , undergoes a transformation such that :  and are the elements of the initial pure state and is the trasmittivity of a fictituous beam splitter mimecking a lossy transmission .we can calculate the evolution of the bell function ( [ b ] ) starting from an initially pure state , described by the elements and and analyzing as a function of the coefficient of transmissivity ( ) .so the bell s function becomes a function  depending on the initial ( pure ) state and transmissivity  of the channel .the relative expression , ideed rather long and complicate , will be used for evaluating the correspondence among experimental results and theory in the next section .in a recent paper ( see ref . ) we have analysed how different entanglement and quantum signatures evolves under decoherence . in this paperwe wish to include the experimental analysis of the non local character under decoherence .we have to stress that , in view of the restrict region ( ) where one could expect a bell inequality violation , we have not observed any bell inequality violation .this is essentially due to the maximum overall transmission we can get from the opo cavity to the homodyne detector ( 63% ) .moreover , we stress that this is rather an a posteriori check of the non - local character of the state than a bell measure .the analysed state is the one outing a sub threshold type ii opo apb2008 .the block scheme of the experiment is given in fig .fig : setup .the full covariance matrix is retrieved by a single homodyne detector following the procedure described in details in ref . .    in fig .[ fig : bellvst ] we have plotted the experimental value obtained for . the continuous line represent the theoretical expections for the pure ancestor state ., the transmittivity of a variable absorber mimicking a realistic transmission channel.,scaledwidth=45.0% ]  as it can be seen experimental data are in good agreement with the expected evolution .different bounds have been , so far , discussed in the literature for discriminating continuous variable separable and entangled states .each of them looks at slightly different facets of the epr paradox .so that , in this paper , they are presented in connection to the original epr arguments .moreover , for the first time , we express by a handy and direct formula a bell type inequaly , written for cv states , in terms of the covariance matrix of a gaussian state .we discuss its relation with the purity of the entangled sub - systems and analyse , also experimentaly , its behaviour under decoherence .so doing we have proved , experimentally , that , also in cv regime , there exists mixed entangled states that do not violate the bell inequality . while , for pure states , any entangled state is bell non local .99        marissa giustina , alexandra mech , sven ramelow , bernhard wittmann , johannes kofler , joern beyer , adriana lita , brice calkins , thomas gerrits , saewoo nam , rupert ursin , and anton zeilinger . . , 497(7448):227230 ,may 9 2013 .vitus hndchen , tobias eberle , sebastian steinlechner , aiko samblowski , torsten franz , reinhard f. werner , and roman schnabel .observation of one - way einstein - podolsky - rosen steering ., 6:596599 , 2012 .

Abstract: entanglement , one of the most intriguing aspects of quantum mechanics , marks itself into different features of quantum states . for this reason different criteria can be used for verifying entanglement . in this paper we review some of the entanglement criteria casted for continuous variable states and link them to peculiar aspects of the original debate on the famous epr paradox . moreover , we give a handy expression for valuating bell type non  locality on gaussian states . we also present the experimental measurement of a particular realization of the bell operator over continuous variable entangled states produced by a sub threshold type  ii opo .


deep neural networks provide a powerful mechanism for learning patterns from massive data , achieving new levels of performance on image classification  , speech recognition  , machine translation  , playing strategic board games  , and so forth .  despite the impressive advances , the widely - used dnn methods still have limitations . the high predictive accuracy has heavily relied on large amounts of labeled data ; and the purely data - driven learning can lead to uninterpretable and sometimes counter - intuitive results  .it is also difficult to encode human intention to guide the models to capture desired patterns , without expensive direct supervision or ad - hoc initialization .  on the other hand, the cognitive process of human beings have indicated that people learn not only from concrete examples ( as dnns do ) but also from different forms of general knowledge and rich experiences . _ logic rules _ provide a flexible declarative language for communicating high - level cognition and expressing structured knowledge .it is therefore desirable to integrate logic rules into dnns , to transfer human intention and domain knowledge to neural models , and regulate the learning process .  in this paper, we present a framework capable of enhancing general types of neural networks , such as convolutional networks ( cnns ) and recurrent networks ( rnns ) , on various tasks , with logic rule knowledge .combining symbolic representations with neural methods have been considered in different contexts .neural - symbolic systems  construct a network from a given rule set to execute reasoning . to exploit _ a priori _ knowledge in general neural architectures , recent work augments each raw data instance with useful features  , while network training , however , is still limited to instance - label supervision and suffers from the same issues mentioned above .besides , a large variety of structural knowledge can not be naturally encoded in the feature - label form .our framework enables a neural network to learn simultaneously from labeled instances as well as logic rules , through an _ iterative rule knowledge distillation _procedure that transfers the structured information encoded in the logic rules into the network parameters .since the general logic rules are complementary to the specific data labels , a natural `` side - product '' of the integration is the support for semi - supervised learning where unlabeled data is used to better absorb the logical knowledge .methodologically , our approach can be seen as a combination of the knowledge distillation  and the posterior regularization ( pr ) method  . in particular , at each iteration we adapt the posterior constraint principle from pr to construct a rule - regularized _ teacher _ , and train the _ student _ network of interest to imitate the predictions of the teacher network .we leverage soft logic to support flexible rule encoding .we apply the proposed framework on both cnn and rnn , and deploy on the task of sentiment analysis ( sa ) and named entity recognition ( ner ) , respectively . with only a few ( one or two ) very intuitive rules , both the distilled networks and the joint teacher networksstrongly improve over their basic forms ( without rules ) , and achieve better or comparable performance to state - of - the - art models which typically have more parameters and complicated architectures .to the best of our knowledge , this is the first work to integrate logic rules with general workhorse types of deep neural networks in a principled framework .the encouraging results indicate our method can be potentially useful for incorporating richer types of human knowledge , and improving other application domains .combination of logic rules and neural networks has been considered in different contexts .neural - symbolic systems  , such as kbann  and cilp++  , construct network architectures from given rules to perform reasoning and knowledge acquisition .a related line of research , such as markov logic networks  , derives probabilistic graphical models ( rather than neural networks ) from the rule set .  with the recent success of deep neural networks in a vast variety of application domains ,it is increasingly desirable to incorporate structured logic knowledge into general types of networks to harness flexibility and reduce uninterpretability .recent work that trains on extra features from domain knowledge , while producing improved results , does not go beyond the data - label paradigm . uses a specialized training procedure with careful ordering of training instances to obtain an interpretable neural layer of an image network . develops a generative model jointly over data - labels and similarity knowledge expressed in triplet format to learn improved disentangled representations .though there do exist general frameworks that allow encoding various structured constraints on latent variable models  , they either are not directly applicable to the nn case , or could yield inferior performance as in our empirical study . transfers predictive power of pre - trained structured models to unstructured ones in a pipelined fashion .our proposed approach is distinct in that we use an iterative rule distillation process to effectively transfer rich structured knowledge , expressed in the declarative first - order logic language , into parameters of general neural networks .we show that the proposed approach strongly outperforms an extensive array of other either ad - hoc or general integration methods .in this section we present our framework which encapsulates the logical structured knowledge into a neural network .this is achieved by forcing the network to emulate the predictions of a rule - regularized teacher , and evolving both models iteratively throughout training ( section [ sec : distill ] ) .the process is agnostic to the network architecture , and thus applicable to general types of neural models including cnns and rnns .we construct the teacher network in each iteration by adapting the posterior regularization principle in our logical constraint setting ( section [ sec : teacher ] ) , where our formulation provides a closed - form solution . figure [ fig : arch ] shows an overview of the proposed framework .our approach allows neural networks to learn from both specific examples and general rules .here we give the settings of these `` learning resources '' .assume we have input variable and target variable . for clarity ,we focus on -way classification , where is the -dimensional probability simplex and is a one - hot encoding of the class label .however , our method specification can straightforwardly be applied to other contexts such as regression and sequence learning ( e.g. , ner tagging , which is a sequence of classification decisions ) .the training data is a set of instantiations of .further consider a set of first - order logic ( fol ) rules with confidences , denoted as , where is the rule over the input - target space , and  ] instead of , and the boolean logic operators are reformulated as : here and are two different approximations to logical conjunction  : is useful as a selection operator ( e.g. , when , and when ) , while is an averaging operator .a neural network defines a conditional probability by using a softmax output layer that produces a -dimensional soft prediction vector denoted as .the network is parameterized by weights .standard neural network training has been to iteratively update to produce the correct labels of training instances . to integrate the information encoded in the rules , we propose to train the network to also imitate the outputs of a rule - regularized projection of , denoted as , which explicitly includes rule constraints as regularization terms . in each iteration constructed by projecting into a subspace constrained by the rules , and thus has desirable properties .we present the construction in the next section .the prediction behavior of reveals the information of the regularized subspace and structured rules .emulating the outputs serves to transfer this knowledge into . the new objective is then formulated as a balancing between imitating the soft predictions of and predicting the true hard labels : where denotes the loss function selected according to specific applications ( e.g. , the cross entropy loss for classification ) ; is the soft prediction vector of on at iteration ; and is the imitation parameter calibrating the relative importance of the two objectives .  a similar imitation procedure has been used in other settings such as model compression  where the process is termed _distillation_. following them we call the `` student '' and the `` teacher '' , which can be intuitively explained in analogous to human education where a teacher is aware of systematic general rules and she instructs students by providing her solutions to particular questions ( i.e. , the soft predictions ) .an important difference from previous distillation work , where the teacher is obtained beforehand and the student is trained thereafter , is that our teacher and student are learned simultaneously during training .  though it is possible to combine a neural network with rule constraints by projecting the network to the rule - regularized subspace after it is fully trained as before with only data - label instances , or by optimizing projected network directly , we found our iterative teacher - student distillation approach provides a much superior performance , as shown in the experiments .moreover , since distills the rule information into the weights instead of relying on explicit rule representations , we can use for predicting new examples at test time when the rule assessment is expensive or even unavailable ( i.e. , the _ privileged information _ setting  ) while still enjoying the benefit of integration .besides , the second loss term in eq . can be augmented with rich unlabeled data in addition to the labeled examples , which enables _ semi - supervised _ learning for better absorbing the rule knowledge .we now proceed to construct the teacher network at each iteration from .the iteration index is omitted for clarity .we adapt the posterior regularization principle in our logic constraint setting .our formulation ensures a closed - form solution for and thus avoids any significant increases in computational overhead .recall the set of fol rules .our goal is to find the optimal that fits the rules while at the same time staying close to .for the first property , we apply a commonly - used strategy that imposes the rule constraints on through an expectation operator .that is , for each rule ( indexed by ) and each of its groundings ( indexed by ) on , we expect =1 ] which is a proper soft truth value .the list rule can span multiple sentences ( within the same document ) .we found the teacher network that enables explicit joint inference provides much better performance over the distilled student network ( section [ sec : exp ] ) .we validate our framework by evaluating its applications of sentiment classification and named entity recognition on a variety of public benchmarks . by integrating the simple yet effective rules with the base networks ,we obtain substantial improvements on both tasks and achieve state - of - the - art or comparable results to previous best - performing systems .comparison with a diverse set of other rule integration methods demonstrates the unique effectiveness of our framework .our approach also shows promising potentials in the semi - supervised learning and sparse data context .  throughout the experiments we set the regularization parameter to . in sentiment classificationwe set the imitation parameter to , while in ner to downplay the noisy listing rule .the confidence levels of rules are set to , except for hard constraints whose confidence is . for neural network configuration , we largely followed the reference work , as specified in the following respective sections .all experiments were performed on a linux machine with eight 4.0ghz cpu cores , one tesla k40c gpu , and 32 gb ram .we implemented neural networks using theano , a popular deep learning platform .we test our method on a number of commonly used benchmarks , including * 1 ) sst2 * , stanford sentiment treebank which contains 2 classes ( negative and positive ) , and 6920/872/1821 sentences in the train / dev / test sets respectively .following we train models on both sentences and phrases since all labels are provided . *2 ) mr * , a set of 10,662 one - sentence movie reviews with negative or positive sentiment . *3 ) cr * , customer reviews of various products , containing 2 classes and 3,775 instances . for mr and cr ,we use 10-fold cross validation as in previous work . in each of the three datasets , around 15% sentencescontains the word `` but '' .  for the base neural network we use the `` non - static '' version in with the exact same configurations .specifically , word vectors are initialized using word2vec and fine - tuned throughout training , and the neural parameters are trained using sgd with the adadelta update rule .r l200pt l40pt l60pt l55pt & model & sst2 & mr & cr + 1 & cnn  & 87.2 & 81.3.1 & 84.3.2 + 2 & cnn - rule- & 88.8 & 81.6.1 & 85.0.3 + 3 & cnn - rule- & 89.3 & * 81.7.1 * & * 85.3.3 * + 4 & mgnc - cnn  & 88.4 & & + 5 & mvcnn  & * 89.4 * & & + 6 & cnn - multichannel  & 88.1 & 81.1 & 85.0 + 7 & paragraph - vec  & 87.8 & & + 8 & crf - pr  & & & 82.7 + 9 & rntn  & 85.4 & & + 10 & g - dropout  & & 79.0 & 82.1 +   table [ tab : sent ] shows the sentiment classification performance .rows 1 - 3 compare the base neural model with the models enhanced by our framework with the `` but''-rule ( eq . ) .we see that our method provides a strong boost on accuracy over all three datasets .the teacher network further improves over the student network , though the student network is more widely applicable in certain contexts as discussed in sections [ sec : distill ] and [ sec : implement ] .rows 4 - 10 show the accuracy of recent top - performing methods . on the mr and cr datasets ,our model outperforms all the baselines .on sst2 , mvcnn  ( row 5 ) is the only system that shows a slightly better result than ours .their neural network has combined diverse sets of pre - trained word embeddings ( while we use only word2vec ) and contained more neural layers and parameters than our model .  to further investigate the effectiveness of our framework in integrating structured rule knowledge , we compare with an extensive array of other possible integration approaches .table [ tab : sent - internal ] lists these methods and their performance on the sst2 task .we see that : 1 ) although all methods lead to different degrees of improvement , our framework outperforms all other competitors with a large margin .2 ) in particular , compared to the pipelined method in row 6 which is in analogous to the structure compilation work  , our iterative distillation ( section [ sec : distill ] ) provides better performance .another advantage of our method is that we only train one set of neural parameters , as opposed to two separate sets as in the pipelined approach .3 ) the distilled student network `` -rule- '' achieves much superior accuracy compared to the base cnn , as well as `` -project '' and `` -opt - project '' which explicitly project cnn to the rule - constrained subspace .this validates that our distillation procedure transfers the structured knowledge into the neural parameters effectively .the inferior accuracy of `` -opt - project '' can be partially attributed to the poor performance of its neural network part which achieves only 85.1% accuracy and leads to inaccurate evaluation of the `` but''-rule in eq ..r l l & model & accuracy ( % ) + 1 & cnn  & 87.2 + 2 & -but - clause & 87.3 + 3 & --reg & 87.5 + 4 & -project & 87.9 + 5 & -opt - project & 88.3 + 6 & -pipeline & 87.9 + 7 & -rule- & 88.8 + 8 & -rule- & * 89.3 * +  r l l l l l & data size & 5% & 10% & 30% & 100% + 1 & cnn & 79.9 & 81.6 & 83.6 & 87.2 + 2 & -rule- & 81.5 & 83.2 & 84.5 & 88.8 + 3 & -rule- & 82.5 & 83.9 & 85.6 & * 89.3 * + 4 & -semi - pr & 81.5 & 83.1 & 84.6 & + 5 & -semi - rule- & 81.7 & 83.3 & 84.7 & + 6 & -semi - rule- & * 82.7 * & * 84.2 * & * 85.7 * & +  we next explore the performance of our framework with varying numbers of labeled instances as well as the effect of exploiting unlabeled data .intuitively , with less labeled examples we expect the general rules would contribute more to the performance , and unlabeled data should help better learn from the rules .this can be a useful property especially when data are sparse and labels are expensive to obtain .table [ tab : sent - semi ] shows the results .the subsampling is conducted on the sentence level .that is , for instance , in `` 5% ''we first selected 5% training sentences uniformly at random , then trained the models on these sentences as well as their phrases .the results verify our expectations .1 ) rows 1 - 3 give the accuracy of using only data - label subsets for training . in every settingour methods consistently outperform the base cnn .2 ) `` -rule- '' provides higher improvement on 5% data ( with margin 2.6% ) than on larger data ( e.g. , 2.3% on 10% data , and 2.0% on 30% data ) , showing promising potential in the sparse data context .3 ) by adding unlabeled instances for semi - supervised learning as in rows 5 - 6 , we get further improved accuracy .4 ) row 4 , `` -semi - pr '' is the posterior regularization  which imposes the rule constraint through only unlabeled data during training .our distillation framework consistently provides substantially better results .we evaluate on the well - established conll-2003 ner benchmark  , which contains 14,987/3,466/3,684 sentences and 204,567/51,578/46,666 tokens in train / dev / test sets , respectively .the dataset includes 4 categories , i.e. , _ person , location , organization _ , and _misc_. bioes tagging scheme is used .around 1.7% named entities occur in lists .we use the mostly same configurations for the base blstm network as in , except that , besides the slight architecture difference ( section [ sec : ner ] ) , we apply adadelta for parameter updating .glove  word vectors are used to initialize word features . l l@ & model & f1 + 1 & blstm & 89.55 + 2 & blstm - rule - trans & : 89.80 ,  : 91.11 + 3 & blstm - rules & : 89.93 ,  : * 91.18 * + 4 & nn - lex  & 89.59 + 5 & s - lstm  & 90.33 + 6 & blstm - lex  & 90.77 + 7 & blstm - crf  & 90.94 + 8 & joint - ner - el  & 91.20 + 9 & blstm - crf  & * 91.21 * +   table [ tab : ner ] presents the performance on the ner task . by incorporating the bi - gram transition rules ( row 2 ) ,the joint teacher model achieves 1.56 improvement in f1 score that outperforms most previous neural based methods ( rows 4 - 7 ) , including the blstm - crf model  which applies a conditional random field ( crf ) on top of a blstm in order to capture the transition patterns and encourage valid sequences . in contrast , our method implements the desired constraints in a more straightforward way by using the declarative logic rule language , and at the same time does not introduce extra model parameters to learn .further integration of the list rule ( row 3 ) provides a second boost in performance , achieving an f1 score very close to the best - performing systems including joint - ner - el  ( row 8) , a probabilistic graphical model optimizing ner and entity linking jointly with massive external resources , and blstm - crf  , a combination of blstm and crf with more parameters than our rule - enhanced neural networks .  from the tablewe see that the accuracy gap between the joint teacher model and the distilled student is relatively larger than in the sentiment classification task ( table [ tab : sent ] ) .this is because in the ner task we have used logic rules that introduce extra dependencies between adjacent tag positions as well as multiple instances , making the explicit joint inference of useful for fulfilling these structured constraints .we have developed a framework which combines deep neural networks with first - order logic rules to allow integrating human knowledge and intentions into the neural models . in particular, we proposed an iterative distillation procedure that transfers the structured information of logic rules into the weights of neural networks .the transferring is done via a teacher network constructed using the posterior regularization principle .our framework is general and applicable to various types of neural architectures . with a few intuitive rules ,our framework significantly improves base networks on sentiment analysis and named entity recognition , demonstrating the practical significance of our approach .though we have focused on first - order logic rules , we leveraged soft logic formulation which can be easily extended to general probabilistic models for expressing structured distributions and performing inference and reasoning .we plan to explore these diverse knowledge representations to guide the dnn learning .the proposed iterative distillation procedure also reveals connections to recent neural autoencoders  where generative models encode probabilistic structures and neural recognition models distill the information through iterative optimization  .the encouraging empirical results indicate a strong potential of our approach for improving other application domains such as vision tasks , which we plan to explore in the future .finally , we also would like to generalize our framework to automatically learn the confidence of different rules , and derive new rules from data .we thank the anonymous reviewers for their valuable comments . this work is supported by nsf iis1218282 , nsf iis1447676 , air force fa8721 - 05-c-0003 , and fa8750 - 12 - 2 - 0342 .we provide the detailed derivation for solving the problem in eq . , section [ sec : teacher ] , which we repeat here : ) \leq \xi_{l , g_l } \\ & \ g_l = 1 , \dots , g_l,\ \l = 1 , \dots ,l , \end{split}\ ] ]   the lagrangian is where - \xi_{l , g_l } \right ) + \alpha(\sum_{{{{\boldsymbol{\mathbf{}}}}}{y}}q({{{\boldsymbol{\mathbf{}}}}}{y}|{{{\boldsymbol{\mathbf{}}}}}{x } ) - 1 ) \end{split}\ ] ] solving eq . , we obtain + \alpha = 0\\ & \qquad\qquad\longrightarrow\qquad q({{{\boldsymbol{\mathbf{}}}}}{y}|{{{\boldsymbol{\mathbf{}}}}}{x } ) = \frac{p_\theta({{{\boldsymbol{\mathbf{}}}}}{y}|{{{\boldsymbol{\mathbf{}}}}}{x } ) \exp\left\{-\sum_{l}\eta_{l}\lambda_{l}(1-r_{l , g_l}({{{\boldsymbol{\mathbf{}}}}}{x},{{{\boldsymbol{\mathbf{}}}}}{y}))\right\}}{e\exp(\alpha ) } \end{split}\ ] ]       we design a simple pattern - matching based method to identify lists and counterparts in the ner task .we ensure high precision and do not expect high recall .in particular , we only retrieve lists that with the pattern `` 1 . ...3 . ... '' ( i.e. , indexed by numbers ) , and `` - ... - ... - ... '' ( i.e. , each item marked with `` - '' ) .we require at least 3 items to form a list .we further require the text of each item follows certain patterns to ensure the text is highly likely to be named entities , and rule out those lists whose item text is largely free text .specifically , we require 1 ) all words of the item text all start with capital letters ; 2 ) referring the text between punctuations as `` block '' , each block includes no more than 3 words .we detect both intra - sentence lists and inter - sentence lists in documents .we found the above patterns are effective to identify true lists .a better list detection method is expected to further improve our ner results .

Abstract: combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models . we propose a general framework capable of enhancing various types of neural networks ( e.g. , cnns and rnns ) with declarative first - order logic rules . specifically , we develop an iterative distillation method that transfers the structured information of logic rules into the weights of neural networks . we deploy the framework on a cnn for sentiment analysis , and an rnn for named entity recognition . with a few highly intuitive rules , we obtain substantial improvements and achieve state - of - the - art or comparable results to previous best - performing systems .


complex robotic coordination tasks in highly uncertain environments require the system designers to take advantage of human operator s strengths , high - level decision - making and flexibility .motivated by these needs , semi - autonomous operation of robots is gaining increasing research interests .one of the most promising design tools for such semi - autonomous systems is passivity , as confirmed in the history of a traditional semi - autonomous robot control problem , bilateral teleoperation - . in this research field ,the human operator has been treated as a passive component and then control architectures have been established while ensuring closed - loop stability based upon this assumption .this paradigm has also been taken in teleoperation of multiple networked robots .rodriguez - seda et al . present an architecture such that the robotic network is controlled by operating a leader robot so that the robots forms a specified formation while avoiding collisions .liu extends motion synchronization on the joint space to the task space under time - varying delays .fully distributed control algorithms are presented by franchi et al . , where stability is ensured in the presence of split and join events .other interesting extensions of bilateral teleoperation are presented in and .varnell and zhang employ a non - classical human - robot interfaces , namely a tablet , and discuss the stability while assuming a human pointing model .saeidi et al . introduce the notion of robot - to - human trust and mixed initiative control scheme in order to improve the performance and reduce workload of the operator .while the above papers consider robot dynamics together with force feedback , the authors studied another problem formulation focusing on interactions between a human operator and kinematic robots as in .the schematic of the intended system is illustrated in fig .[ fig : scenario ] .then , we investigated motion synchronization of robots to human references under distributed information exchange between the human and robots , and among robots . to this end , we presented a novel passivity - based control architecture and proved synchronization under explicit bilateral connections between the human and robotic network .for implementation on real robotic systems , both the human - robotic network and inter - robot interactions must be implemented using appropriate communication technology . in this case, the communication channels may suffer from delays in the transmission of information , which is indeed one of the most important issues in bilateral teleoperation .however , did not address this issue explicitly .our objective is thus to extend the results of to the case with time delays and its experimental studies .although both the human - robotic network and inter - robot communications may have delays , this paper investigates the latter since this issue emerges in the one - human - multiple - robot interactions while the former has been in - depth studied in bilateral teleoperation .delays in inter - robot communications have been extensively studied in the field of cooperative control ( see and references therein ) . among many approaches ,this paper focuses on the scheme presented in , and synchronization is guaranteed despite the delays . in this paper , the control architecture in shown to be successfully integrated with the cooperative control for human - robotic networks presented in .however , the integration is not straightforward and requires novel technical extensions in the formulation and this is presented in this paper .furthermore , as pointed out in , real deployments of robotic network is important from the viewpoint of difficulties to simulate each intended task and situation faithfully .therefore , we investigate our proposed architecture in a testbed and show the influences of communication delays not only on a robotic network but also on a real human s behaviour .  the organization of this paper is as follows : section [ sec : problem ] presents the intended problem and briefly reviews the results of . in section [ sec : hrn ] , we design a novel control architecture based on the scattering transformation , and then , show passivity of the resulted system .we also show position synchronization to the reference values in section [ sec : main ] .we demonstrate our results through experiments in section [ sec : experiment ] , and finally , summarize the obtained results in section [ sec : conclusions ] .in this section , we start by reviewing the problem formulation and results presented in . please refer to for more details .let us consider a system with a human operator and mobile robots located on a 2-d plane as shown in fig .[ fig : scenario ] .we suppose that the motion of every -th robot is described by the kinematic model where and are the position and velocity input of -th robot , respectively .  every robot can interact with neighboring robots and the inter - robot information exchanges are modeled by a graph . then , robot has access to information of the robots belonging to the set . throughout this paper , we assume the communication graph is fixed , undirected and connected . differently from , we assume that the inter - robot communication suffers from time delays , which will be discussed in section [ sec : problem ] .in addition to the total robots set , we define accessible robots set which is a subset of ( fig .[ fig : scenarioblock ] ) ._ accessibility _ means that the operator can send a signal to and receive feedback information from only the robots in . here, we assume that the human operator determines a command signal based on certain information visually fed back from through a monitor in front of the operator . the command is then sent back to all the accessible robots .we also introduce the notation such that if and otherwise .  in this paper , we address position synchronization .let us assume that the human operator has a desired position denoted by .then , the goal of the position synchronization is defined by the objective here is to design the robot controller and the information displayed on the monitor so as to guarantee the above control goal .the authors take the control input as then , the signal to achieve inter - agent motion synchronization is designed as where  , if and otherwise .then , the collective dynamics ( [ eq : integrator ] ) , ( [ eqn : hata ] ) and ( [ eq : uriorig ] ) for all is passive from to , where is defined as and is the number of elements of .based on this passivity , we let the feedback information for the human operator be .namely , the human operator can obtain the average position of the accessible robots . in , position synchronizationis theoretically proved in the absence of delays under a passivity assumption on the human s decision process together with some additional assumptions .however , inter - robot communication delays may destabilize the above control system .this is why we present a system architecture with robustness against inter - robot communication delays .the system architecture ( [ eq : xiorig ] ) , ( [ eq : uriorig ] ) can achieve not only position synchronization but also synchronization of velocity at the same time , i.e. , where is a constant reference velocity .however , we omit this part because of space limitations .-th robot and its cooperative controller including the scattering transformation.,width=283 ]   in this section , we redesign the cooperative controller generating in order to guarantee stability and synchronization despite the inter - robot communication delays .  in the presence of the delays ,-th robot can not obtain and at time .we thus replace these signals by , respectively .then , -th robot s dynamics is described by let us now define as -  \left [ \begin{array}{cc } \ !q_{i } \ ! \\ \ !\xi_{i } \ !\end{array } \right ] \right ) = m_{ij } \left [ \begin{array}{cc } \ !r^{q}_{ij } - q_{i } \ ! \\ \ !r^{\xi}_{ij } - \xi_{i } \ !\end{array } \right ] , \label{eq : vij}\end{aligned}\ ] ] where  ] .  from the above discussions , the system ( [ eq : xii ] ) and ( [ eq : uri ] ) can be reduced to a feedback interconnection of passive systems and a collection of passive maps .accordingly , we can obtain the following inequality for each robot dynamics , \sum_{j \in { \mathcal{n}}_{i}}p_{ij } \nonumber \\ = &  -\!\ !{ \mathcal{n}}_{i}}a_{ij}\|q_{i } - r^{q}_{ij}\|^{2 }  \!+\ !\sum_{j \in { \mathcal{n}}_{i } } r_{ij}^{t } p_{ij }  \leq \sum_{j \in { \mathcal{n}}_{i}}r_{ij}^{t } p_{ij}. \label{eq : rijvij}\end{aligned}\ ] ] the above inequality implies that each robot dynamics is passive from the stacked vector of to the stacked vector of from all neighbor robots with respect to the storage function ( [ eq : si ] ) .   and robot .,width=328 ]   in this subsection , we present a novel control architecture based on . hereafter , similarly to , we assume that reference is constant , which means that we are assuming that these signals are varying so slowly that the analyses under the constant reference are applicable to the actual system .time varying reference is also addressed in , however its extension to the case with delays is left as a future work .  following the architecture of ,we let each agent exchange the variable through scattering transformation instead of directly sending and as illustrated in fig .[ fig : roboti ] . in the present case ,the scattering variables are defined as where ^{t} ] and the storage function for the communication channel as thus , if we define and ^{t} ] and ^{t} ] .then , the lasalle s invariance principle for time delay systems is applicable and any solution of the system converges to the largest invariant set in the set of functions satisfying .thus , means and .hence , we can conclude as follows . next , in order to analyze further , we need to follow the behavior of .first , we define and as    then , each element of ( [ eq : s1])([eq : st2 ] ) can be given as furthermore , subtracting ( [ eq : rqji ] ) at time from ( [ eq : rqij ] ) yields utilizing the equations in ( [ eq : rxiij ] ) , we have .now , according to ( [ eq : rqconv ] ) , the signals and converge to , i.e. , holds .thus , taking the limit of ( [ eq : rijrij ] ) yields the same equation holds for as on the other hand , because the signal for all converges to from ( [ eq : rqconv ] ) , we obtain subtracting ( [ eq : rikrik2 ] ) from ( [ eq : rijrij2 ] ) and using ( [ eq : rijrik ] ) , we have because of ( [ eq : rqconv ] ) , equation ( [ eq : rjirki ] ) implies , which holds for .then , we have for all . furthermore , from ( [ eq : zqconv ] ) , we have therefore , we can conclude that for all .this completes the proof .  as in the same way ,the velocity synchronization ( [ eq : goal2 ] ) is achieved with the same control architecture .however , we omit the result because of space limitations .in this section , we show the experiment results of the discussed control system . in this paper , we focus on the influence of the communication delay on the human operator s behavior . for that purpose ,we conduct two types of experiments , without inter - robot communication delay and with inter - robot communication delay . then, we investigate the differences by comparing the robots trajectories and human input . although it is also important to investigate the human passivity assumption , as already mentioned in section [ sec : main ] , we leave this as a future work .                   in this subsection, we introduce our experiment system and the intended scenario .the architecture of experiment system is illustrated in fig .[ fig : expsys ] .we use 6 omnidirectional robots named tdo48 from tosadenshi inc . and obtain image data by using a ceiling camera named firefly mv from point grey . from image processing by c++ , we obtain all robots positions . even though the control architecture is implementable by each robot processor, we artificially implement all cooperative controller in a computer for simplicity .the inter - robot communication delays are also generated in simulink and the delays set 0.5s .simulink is running on dspace for the real time implementation . on the other hand, we show the average position of accessible robots and given reference position via gui programmed by c++ .then , the participant inputs velocity command through mouse . finally , the velocity inputs are converted to motor angular velocities , and then , transmitted to each robot via bluetooth .  for the scenario, we ask the participant to control robotic network to a given position , as shown by red dot in fig .[ fig : expfield ] .the reference position is ^{t} ] . during this section , we show all figures using the biased positions , rather than the real positions .the communication graph of the robotic network is shown in fig .[ fig : expfield ] .the initial positions of all robots are ^{t}$ ] and .the parameters are set as and .first , the result without inter - robot communication delay is shown in fig .[ fig : expresult1 ] .the human operator successfully control the accessible robots , and all robots reached the target position .note that non - accessible robots could close the distances with the accessible robots around 30s while the accessible robots are still moving .this shows one of the advantage in exchanging the integral value , , of .the human input is shown in the bottom part of fig .[ fig : expresult1 ] .the result shows that the human operator smoothly controlled the robotic network .next , we show the result with inter - robot communication delay and the scattering transformation in fig . [fig : expresult2 ] . in the same way as the delay free case, all robots reached the target position .however , comparing the trajectories with the result without delay , non - accessible robots could nt close the distances with the accessible robots . as a result , the accessible robots moved back and forth around the reference position . the arrival time is delayed by about 70s .the human input is shown in the bottom of fig .[ fig : expresult2 ] .after 50s , the human operator repeated adjustments because non - accessible robots followed late . comparing to the result of delay free case ,the human input looks more fluctuated , which can be interpreted as the deterioration of human s operability .  in summary ,position synchronization by the proposed architecture is verified through this experiment .in addition to this result , since we observed performance degradation of human , thorough investigation is needed regarding human performance . to this end , we need a criteria to measure the performance qualitatively .in this paper , we have investigated a cooperative control architecture of human - robotic networks in the presence of inter - robot communication delays , where the objective is to guarantee position synchronization to human s desired position .first , we proposed control architecture based on and the scattering transformation .then , we showed passivity of the robotic network .next , by using human passivity assumption , we showed that the feedback system achieves position synchronization .finally , we demonstrated the efficiency of the proposed architecture through experiments , which managed to move all robots to target position in the same way as delay free case .furthermore , we investigated the influences of inter - robot communication delays on human s operability .rodriguez - seda , j.j .troy , c.a .erignac , p. murray , d.m .stipanovic and m.w .spong , `` bilateral teleoperation of multiple mobile agents : coordinated motion and collision avoidance , '' _ ieee trans .control systems technology _ , vol .4 , pp . 984992 , 2010 .a. franchi , c. secchi , h.i .son , h.h bulthoff and p.r .giordano , `` bilateral teleoperation of groups of mobile robots with time - varying topology , '' _ ieee trans .robotics _ , vol .5 , pp . 10191033 , 2012 .p. varnell and f. zhang , `` dissipativity - based teleoperation with time - varying communication delays , '' _ proc .4th workshop on distributed estimation and control in networked systems _ , pp .369376 , 2013 .h. saeidi , f. mclane , b. sadrfaidpour , e. sand , s. fu , j. rodriguez , j.r .wagner and y. wang , `` trust - based mixed - initiative teleoperation of mobile robots , '' _ proc .2016 american control conference _ , pp . 61776182 , 2016 .y. morita , y. ogawa , y. kawai , t. imamura , t. miyoshi and k. terashima , `` design method for multilateral tele - control to realize shared haptic mouse , '' _ proc .sice annual conference 2013 _ , pp . 22202226 , 2013 .s. hu , c. chan and y. liu , `` event - triggered control for bilateral teleoperation with time delays , '' _ proc .2016 ieee / rsj international conference on advanced intelligent mechatronics _ , pp . 16341639 , 2016 .m. shahbazi , h.a .talebi and m.j .yazdanpanah , `` a control architecture for dual user teleoperation with unknown time delays : a sliding mode approach , '' _ proc .2010 ieee / rsj international conference on advanced intelligent mechatronics _ , pp . 12211226 , 2015 .t. hatanaka , n. chopra and m. fujita , `` passivity - based bilateral human - swarm - interactions for cooperative robotic networks and human passivity analysis , '' _ proc .54th ieee conference on decision and control _ , pp . 10331039 , 2015 .t. hatanaka , n. chopra , j. yamauchi and m. fujita , `` a passivity - based approach to human - swarm collaborations and passivity analysis of human operators , '' _ trends in control and decision - making for human - robot collaboration systems _ , y. wang and f. zhang ( eds . ) , springer - verlag , 2017 .  m. egerstedt , j .-de la croix , h. kawashima and p. kingston , `` interacting with networks of mobile agents , '' large - scale networks in engineering and life sciences , pp .199224 , springer - verlag , 2014 .d. sieber , s. music and s. hirche , `` multi - robot manipulation controlled by a human with haptic feedback , '' _ proc .2015 ieee / rsj international conference on intelligent robots and systems _ , pp . 24402446 , 2015 .

Abstract: in this paper , we present experimental studies on a cooperative control system for human - robotic networks with inter - robot communication delays . we first design a cooperative controller to be implemented on each robot so that their motion are synchronized to a reference motion desired by a human operator , and then point out that each robot motion ensures passivity . inter - robot communication channels are then designed via so - called scattering transformation which is a technique to passify the delayed channel . the resulting robotic network is then connected with human operator based on passivity theory . in order to demonstrate the present control architecture , we build an experimental testbed consisting of multiple robots and a tablet . in particular , we analyze the effects of the communication delays on the human operator s behavior .


game theory as a sub field in mathematics has enjoyed a tremendous growth and has been applied to wide range of fields such as economics , political science , biology , and computer science .the successful application of the theory in the classical context inspired formulation of quantum games . one key feature of a quantum game is that there are an infinite number of strategies possible , which can potentially lead to far more equilibria . in quantum game theory ,concepts from quantum information theory are applied to game theory such that qubits represent the states of each player , quantum gates ( unitaries ) are used for implementing strategies , and entanglement is used to mediate communication between the players .considerable interest was generated in this field when the quantization of a classical game using the eisert - wilkens - lewenstein ( ewl ) formalism showed that the classical prisoner s dilemma ( pd ) could be resolved by including a new quantum strategy that is not available in the classical game .we employ the ewl formalism primarily because it is widely used in the literature .this formalism quantizes the strategy space of a classical game as opposed to other approaches where the payoff function is quantized , which can be advantageous for directly comparing a quantum game to mixed strategy classical games .extension of a classical game into a quantum context gives rise to entirely new classes of games , depending on how that extinsion is made , and our focus here is again on games based on ewl formalism .there is also distinction between quantizing a classical game and gaming a quantum system as the former is concerned with applying quantum information to game theory , with the goal to learn something about the game that is produced , whereas the latter applies the rules of game theory to quantum physics , with the goal of learning something about the underlying physics .our approach is the former .  in this workwe are focused on quantizing classical bayesian games that have players with incomplete knowledge about the payoff functions of their opponents .the uncertainty in knowledge of the players is encoded in types and priors or beliefs as classical probability distributions on types .formally , a classical two person bayesian game is a tuple where , represent the state and action spaces of the player , is space of types from which nature assigns one member for each player .lack of knowledge on the types makes this space a random variable and each player has priors or beliefs about it in the form of a probability distribution on it which is encoded in the probability measure .this results in players choosing a strategy from conditioned on the types and the cost function is a mapping on . later, we describe the quantum version of this bayesian set up , where the priors are still classical but and are based on quantum information .our approach is similar in spirit to the quantized bayesian game of battle of sexes where the probabilities are calculated in accordance with quantum mechanics and the priors are classical , however , their approach relies only on probability distributions , our approach retains the quantum mechanical formalisms of state vectors and operators .the primary advantage a quantum game has over its classical counterpart may be seen in the case of pd .when the initial state is maximally entangled , and the strategy space is restricted to those in the original ( ewl ) formalism , the payoff for the players at the nash equilibrium ( ne ) in the quantum game exceeds the payoff of the players at the ne in the classical counterpart .the ne is the set of strategies where no player can benefit by unilaterally changing their strategy .it is possible in the classical game for the prisoners to choose strategies corresponding to a pareto efficient ( pe ) solution which gives higher payoff than the ne , though this is only with cooperation or a contract , which require communication and can be broken .a pe solution is a set of strategies where no player can benefit without , unilaterally or not , hurting the other .a second key feature of quantum games is that the player s initial states can be entangled .though we only look at non - cooperative games where the players act rationally and only in their self interest , the entanglement can ensure that the outcome of the player s strategy choices are correlated in a quantum mechanical way .once established , these correlations persist even if the players can not communicate , exhibiting the non - local characteristic of quantum mechanics . in some cases, the correlations produced from entanglement can not be described classically .the role of entanglement in a quantum game has been interpreted as a form of advice , contract , or mediated communication between the players , and is given by the referee . however , in contrast to classical game theory , the advice or contract is established before the players make their strategy choices by using an initial entangled state , after which , there is no communication between the players , and they are physically prohibited from breaking the contract .entanglement can also be thought of as an environment that acts to correlate the player s choices , since the entanglement is imposed by the referee .the solutions to the game can vary greatly with the amount of entanglement such that new ne form with partial entanglement that are different from those at maximal entanglement or zero entanglement , or can also lead to the complete absence of a ne for an entangled game even when the classical game has a ne , such as in the maximally entangled pd game .games with mixed strategies , that is , when the players choose the strategies with a probability , always have ne solutions , but may not have mixed strategy solutions for every possible probability distribution on the payoff functions . in other wordsthere are distributions over the payoff functions that are not in the image of the mixed version of the original clasical game .one possible way to extend the games to realize other probability distributions over the payoff functions is to set up games where the strategies of the players are correlated by some form of advice or mediated communication . on the other hand, quantum games can realize every possible probability distribution on payoff functions through the use of entanglement which can facilitate correlated strategies .in fact , given one player s strategy the other player can choose strategies such that any possible distribution on the payoff function can be achieved , which can lead to the absense of ne in certain cases , such as in the maximally entangled pd game .  when there is incomplete information available to the players involved , the game can be treated using a bayesian approach .this produces a game that is a classical mixture of two quantum games .bayesian games have seen interest because they can be easily formulated to show a quantum advantage .this can be done by leveraging bell s inequalities such that the payoff function of the game is cast in terms of the expectation values of observables employed in a form of a bell s inequality .thus , by using quantum correlations , a higher payoff at the ne can be achieved than is possible using only classical correlations .this shows the advantage for quantum games when the payoff function has the form of a bell s inequality .we wish to study bayesian games in a more general framework in order to shed light on how the non - local advice via the entanglement , functions in a game with incomplete information .the ability to include multiple agents , allowance for incomplete information , and the incorporation of game theory concepts such as fairness or equilibria make quantum bayesian games a useful tool for quantum network , which features entangled qubits shared non - locally across multiple nodes . when interacting with multiple agents on a network , a game theory analysis is often justified because agents are typically free to make their choices in their best interests , perhaps mitigated by some referee .it is also often the case in interacting with multiple agents on a network , that the players will have incomplete information about the other agents , which rationalizes the approach to include a classical bayesian framework for prior information on a quantum game .the utilization of quantum games on a quantum network could potentially be used in applications such as the analysis of the quantum security protocols , the development of distributed quantum computing algorithms , or using non - locally shared quantum information to improve the efficiency of classical network algorithms .in addition there have been several experimental implementations of the two - player pd game within this framework using nuclear magnetic resonance , quantum circuits in optical , and ion - trap platforms .the structure of the paper is as follows . in section [ sec : classical ]we introduce the classical game we wish to quantize and summarize its solutions . in section [ sec : quantum ]we give some of the theoretical background necessary to employ a bayesian game within a quantum probability space .in section [ sec:1 ] we give details of the method we employ to find the solutions to the quantized game , where we vary the degree of entanglement and amount of incomplete information . in section [ sec:2 ] we present solutions to the two - player games where we find that the structure of each ne is comprised of a class of strategy choices related to one another by a phase relationship , giving rise to a class of ne between the two players . in section [ sec:3 ]we analyze the quantum bayesian game and find that the ne form a phase - diagram like structure in the amount of entanglement , and amount of incomplete information .the ne are found to have a complex and sometimes surprising structure within this phase diagram .finally we offer a discussion of what our results tell us about the role of entanglement and partial information in a quantum bayesian game in section [ sec:4 ] , and end with some conclusions .the bayesian game we considered here is a variation of pd , the district attorney s ( da s ) brother , which involves three players , or equivalently , represents a situation where player b does not know what type player a is . in the first case ,player a and b play the standard pd game . in the second case , player b believes player a is the da s brother which gives player a an advantage resulting in an asymmetric payoff between the players .first , we consider a version of the two - player pd game that is slightly modified from the canonical formulation such that the players have asymmetric payoffs .this has the payoff matrix given by :  [ cols="<,^,>",options="header " , ]   in addition , there are two blocks of parameter space where there are no ne .they are given by  ] and in the region  ] .the interpretation of a ne is that by playing rationally , the players in a game will tend towards playing the ne strategy choices .the ne is stable in that players do not have any incentive to deviate , and is thus self - enforcing .the character of the equilibria that arise when entanglement is present seem to bear resemblance to the concept in classical games of a correlated equilibrium .a correlated equilibrium in classical games is achieved when mixed strategies are employed and there is communication between the players in the form of advice or a contract .if players receive some piece of advice , or react in a predetermined way to a random event , they can employ strategies that are correlated with one another and realize self - enforcing equilibria that are different from those in the mixed game without communication .in contrast , our analysis includes only pure strategies and the role of the advice is played by the initial entanglement .when the player s qubits are entangled , the outcomes of the measurement following their strategy choices will be correlated in a specific way , determined by the type of entanglement .the entanglement is imposed on the players by a referee , and once it is initially established , no communication between the players is necessary , and in fact the players are physically prohibited from breaking the contract .the correlation will also persist even if the players make their strategy choices simultaneously and non - locally .in addition , the specific type of non - classical correlation , enabled by entanglement , can be such that the players can have correlated outputs that are not possible with classical probability distributions in the absence of communication .however , as the amount of entanglement is changed , the effect that the imposed correlation has on the structure of the ne can change dramatically . at zero entanglement , the quantum formulation of the game strongly resembles the classical game , with the players playing quantum strategies that closely resemble the classical strategy choices ( d , d ) . as the entanglement increases, the strategy choices of the ne do not change , rather , they continue to play the same strategies as in the case with no entanglement .thus , the contract enforced by the initial entanglement does not induce the players to play a strategy that is different than the one they would play if there were no entanglement , rather it ensures that the outcome of their strategy choices is correlated in a certain way .the conditions of the ne guarantee that the resulting equilibrium is self - enforcing .  as the degree of entanglement , or amount of correlation , is increased , one might expect that the effective contract is more strictly enforced or that the advice is more closely followed , leading to a larger benefit for the players at equilibrium .this is true for a while , but as in the two - player quantum pd game with symmetric payoffs , the nes are absent above a critical value of entanglement .this is similar to the phase - transition like behavior that has been seen in some quantum games , and should be investigated further .this also contrasts with an intuition of a classical game with correlated equilibrium , where one might expect that the more strictly a contract is enforced , the greater the benefit from that contract .  in the bayesian game , we see evidence of a structure with a much richer and sometimes surprising phase - transition like behavior that can occur both in the amount of entanglement , as has been seen in the two - player games , but also in the amount of incomplete information , i.e. . if only looking at the classical bayesian game , and the two versions of the two - player game , one would not necessarily predict that there is a region in the center with no ne , that new equilibria may appear ( i.e. ) , or how each of the ne will depend on the parameters and without solving for the full possibilities of the game .it is perhaps indicative of the structure of classical probability theory and quantum mechanical probability theory that the payoffs at the ne vary linearly along the classical probability and non - linearly ( i.e. as trigonometric functions ) along the quantum parameter , in which probabilities depend on the square of the components of the player s state ( i.e. wave function ) .the fact that the amount of entanglement can produce abrupt changes in the behavior of a quantum game underscores the importance of decoherence in a quantum game application , as the purity of the initially entangled state could dramatically influence the outcomes and the stability of the game .the behavior of the game can also abruptly changes as a function of the agents prior knowledge in a game , i.e. .this could certainly impact any algorithm taking place on a network , where knowledge of the motivations and abilities of the other agents on the network is incomplete .the structure as a result of the amount of entanglement is due to the constraints imposed by the referee , while the structure in the priors is dependent on the beliefs of the players .both are critical to the structure of the game , however , the referee can constrain the possible equilibria that may be achieved by adjusting the amount of entanglement , even if the player s preferences , i.e. payoffs , and prior knowledge remain unchanged .as stated earlier , each ne solution in the quantum game is an infinite class of equilibria with a fixed phase relationship and equal payoffs .there remains an uncertainty in exactly which equal payoff ne , i.e. which phase , the players will end up playing .this uncertainty can also arise in classical games .in several cases , there are multiple ne that are different payoffs , and that differ by more than just a phase relationship , such as in the da s brother game .the equilibrium in the bayesian game is an example of a ne that does not exist in the two - player games , and can occur simultaneously with other ne .when there are multiple ne , while playing a game , it would be possible for the players to be stuck on a lower payoff ne , as a local maximum in their payoff landscape , neither being willing to deviate .it is interesting to note that in the two - player da s brother game , or with the corresponding ne in the bayesian games , the multiple ne that exist have strategy choices which differ by more than a phase relationship and even correspond to different classical strategy choices . at lower entanglementthey have distinct payoffs , but as the entanglement approaches maximal , the payoff converges to the same value. this could complicate the ne when the two players can not agree on which of the equivalent payoff ne to play .we have classified the solutions to a quantum bayesian game based on the prisoner s dilemma where there are multiple nash equilibria .the phase structure of the game in entanglement and probability space is non - 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Abstract: quantum games with incomplete information can be studied within a bayesian framework . we consider a version of prisoner s dilemma ( pd ) in this framework with three players and characterize the nash equilibria . a variation of the standard pd game is set up with two types of the second prisoner and the first prisoner plays with them with probability and respectively . the bayesian nature of the game manifests in the uncertainty that the first prisoner faces about his opponent s type which is encoded either in a classical probability or in the amplitudes of a wave function . here , we consider scenarios with asymmetric payoffs between the first and second prisoner for different values of the probability , , and the entanglement . our results indicate a class of nash equilibria ( ne ) with rich structures , characterized by a phase relationship on the strategies of the players . the rich structure that can be exploited by the referee to set up rules of the game to push the players towards a specific class of ne . these results provide a deeper insight into the quantum advantages of bayesian games over their classical counterpart .   example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore