Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and the low success probability of finding a global optimal measurement output. Each measurement round requires preparing the quantum system and applying quantum operations and measurements with high-precision control in the physical layer. These issues result in extremely high-cost measurements with a low probability of success at the end of the measurement rounds. Here, we define a novel measurement for quantum computations called dense quantum measurement. The dense measurement strategy aims at fixing the main drawbacks of standard quantum measurements by achieving a significant reduction in the number of necessary measurement rounds and by radically improving the success probabilities of finding global optimal outputs. We provide application scenarios for quantum circuits with arbitrary unitary sequences, and prove that dense measurement theory provides an experimentally implementable solution for gate-model quantum computer architectures.
Quantum measurement has a fundamental role in quantum mechanics with several different theoretical interpretations @cite_11 @cite_84 @cite_46 @cite_81 @cite_40 @cite_65 @cite_51 @cite_3 @cite_62 @cite_74 @cite_33 @cite_41 @cite_30 . The measurement of a quantum system collapses of the quantum system into an eigenstate of the operator corresponding to the measurement. The measurement of a quantum system produces a measurement result, the expected values of measurement are associated with a particular probability distribution.
@cite_30 @cite_62 @cite_33 @cite_41 @cite_65 @cite_84 @cite_3 @cite_40 @cite_81 @cite_74 @cite_46 @cite_51 @cite_11
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The effects of any quantum measurement can be described by a collection of measurement operators l_brace M sub m r_brace acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed. The most efficient way of obtaining information about the state of a quantum system is not always a direct measurement. It is sometimes preferable to extend the original Hilbert space of states into a larger space, and then to perform a quantum measurement in the enlarged space. Such an extension is always possible, by virtue of Neumark's theorem. The physical interpretation usually given to that theorem is the introduction of an auxiliary quantum system, prepared in a standard state, and the execution of a quantum measurement on both systems together. However, this widespread interpretation is unacceptable, because the statistical properties of the supposedly standard auxiliary system are inseparably entangled with those of the original, unknown system. A different method of preparing the auxiliary system is proposed, and shown to be physically acceptable. We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state Φ+ and (2) two spatially separated but otherwise unknown measurement apparatus one on each side, that are each claimed to execute an orthogonal measurement at an angle θ ∈ -π 8, 0, π 8 that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography. Abstract It is a central point in the quantum theory of measurement that it is impossible to discriminate perfectly between two non-orthogonal quantum states if only one physical system is considered. Standard arguments give | p | q > | 2 as the essential quantity that limits the effectiveness of discrimination between | p > and | q >. It is here shown, however, that not | p | q > | 2 but rather | p | q > | plays the role of determining the measure of distinguishability of | p > and | q > if a classification with certainty is required.