We present a general model for quantum channels with memory and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time @math do not depend on inputs at times @math can be decomposed into a concatenated memory channel. We then examine and present different physical setups in which channels with memory may be operated for the transfer of (private) classical and quantum information. These include setups in which either the receiver or a malicious third party have control of the initializing memory. We introduce classical and quantum channel capacities for these settings and give several examples to show that they may or may not coincide. Entropic upper bounds on the various channel capacities are given. For forgetful quantum channels, in which the effect of the initializing memory dies out as time increases, coding theorems are presented to show that these bounds may be saturated. Forgetful quantum channels are shown to be open and dense in the set of quantum memory channels.
Apparently, the first model of a quantum channel with memory was introduced by in 2001: they gave an example of a qubit channel with Markovian correlated noise @cite_29 @cite_1 in which entangled input states may increase the transmission rate for classical information. These results have recently been extended to some bosonic Gaussian channels @cite_51 @cite_21 . Such an effect has been demonstrated experimentally for optical fiber channels with fluctuating birefringence, in which consecutive light pulses undergo strongly correlated polarization transformation @cite_49 @cite_9 . (Whether such examples exist in the memoryless setting is still an open question, and presently considered one of the most eminent open problems of quantum information theory, with wide implications for other problems in the field @cite_27 @cite_2 .)
@cite_29 @cite_21 @cite_1 @cite_9 @cite_27 @cite_49 @cite_2 @cite_51
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In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite-memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no information is lost to the environment, achieving the upper bound implies that the channel is asymptotically noiseless. We present an experiment demonstrating the entanglement enhanced capacity of a quantum channel with correlated noise, modeled by a fiber optic link exhibiting fluctuating birefringence. In this setting, introducing entanglement between two photons is required to maximize the amount of information that can be encoded into their joint polarization degree of freedom. We demonstrated this effect using a fiber-coupled source of entagled photon pairs based on spontaneous parametric down-conversion, and a linear-optics Bell state measurement. The obtained experimental classical capacity with entangled states is equal to @math per a photon pair, and it exceeds approximately 2.5 times the theoretical upper limit when no quantum correlations are allowed. The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real-world communication channels experience noise which is modeled better by errors that are correlated between separate channel uses. In this Brief Report, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channels. We develop a model for a noisy communication channel in which the noise affecting consecutive transmissions is correlated. This model is motivated by fluctuating birefringence of fiber optic links. We analyze the role of entanglement of the input states in optimizing the classical capacity of such a channel, with a constraint that in every use of the channel at most one photon is being transmitted. Assuming a general form of the ensemble for two consecutive transmissions, we derive tight bounds on the classical channel capacity depending on whether the input states used for communication are separable or entangled across different temporal slots. This result demonstrates that by an appropriate choice, the channel capacity may be notably enhanced by exploiting entanglement.