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arXiv:quant-ph/0303178 · Physical Review Letters

Interference of Quantum Channels

Daniel K. L. Oi

Published Aug 7, 2003• 64 citations
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Abstract

We show how interferometry can be used to characterize certain aspects of general quantum processes and, in particular, the coherence of completely positive maps. We derive a measure of coherent fidelity, the maximum interference visibility, and the closest unitary operator to a given physical process under this measure.
DOI
10.1103/physrevlett.91.067902

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Abstract Interference, which has its origin in the superposition principle, is one of the hallmarks of wave mechanics and constitutes a versatile resource for many information processing tasks. As such, it is actually a manifestation of coherence. Despite its long history in the development of physics, quantitative studies of interference are still an important topic. Traditionally, interference is often characterized via the fringe visibility from an operational perspective. This is experimentally convenient. However, from a theoretic perspective, it is desirable to reveal information‐theoretic aspects of interference. In this work, coherence of a state (with respect to a unitary operator parameterized by the interfering paths and phase shifts in multi‐path interference) is first quantified in terms of a generalized version of the Wigner‐Yanase skew information, two natural quantifiers of interference are then introduced via this coherence measure. Basic properties of these quantifiers of interference are further revealed, and the concepts are illustrated through several examples.
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We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a ‘fidelity-like’ lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of a priori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimization of the same quantity called completely bounded process fidelity.
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In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.