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International Journal of Computational Science and Engineering

Unambiguous discrimination of binary coherent states

Wenbin Yu, Zijia Xiong, Shanshan Rong, Yang Liu, Siyao Wang, Yinsong Xu, Alex X. Liu

Published Jan 1, 2020• 1 citation
Publisher

Abstract

Considering quantum detection, there are two different ways to make a measurement on signals set. One is minimum error discrimination and another is unambiguous states discrimination. In this work, we study the unambiguous state discrimination of coherent states. The quantum measurement model investigated is based on binary signals. All necessary positive-operator valued measurements are established to implement the quantum measurements in non-ambiguity way. The conclusive probability and inconclusive probability for the unambiguous discrimination of both on-off keying and binary-phase-shifting keying modulations are derived rigorously to show the measurement performance of proposed detection method theoretically.

DOI
10.1504/ijcse.2020.107353

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Considering quantum detection, there are two different ways to make a measurement on signals set. One is minimum error discrimination and another is unambiguous states discrimination. In this work, we study the unambiguous state discrimination of coherent states. The quantum measurement model investigated is based on binary signals. All necessary positive-operator valued measurements are established to implement the quantum measurements in non-ambiguity way. The conclusive probability and inconclusive probability for the unambiguous discrimination of both on-off keying and binary-phase-shifting keying modulations are derived rigorously to show the measurement performance of proposed detection method theoretically.
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Abstract Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states.
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In this paper, we consider the quantum unambiguous discrimination problem of a set of linearly independent pure states. With a constructive procedure, we establish a necessary and sufficient condition for feasible POVM measurements for unambiguous quantum state discrimination. We develop methods to calculate the optimal discrimination efficiencies for minimizing the inconclusive probability and the optimal discrimination efficiencies for the minimax criterion. Finally, we prove a necessary and sufficient condition to have a feasible POVM measurement which achieves the minimum inconclusive probability criterion and the minimax criterion simultaneously and show that geometrically uniform states with equal a priori probabilities meet this condition.
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