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Physical Review A

Optimal receiver for discrimination of two coherent states with inconclusive results

Kenji Nakahira, Tsuyoshi Sasaki Usuda

Published Nov 26, 2012• 8 citations
Publisher

Abstract

We investigate the implementation of a measurement for binary optical coherent states that minimizes the error probability with a fixed rate of an inconclusive result. As a special case, the optimal measurement without inconclusive results, which is expressed as a projective measurement, can be implemented using only a beam splitter, a local coherent light source, a photon detector, and a feedback circuit. We find that the optimal measurement for binary optical coherent states with any probability of an inconclusive result can be implemented by the same optical components, even though the measurement is generally not projective.

DOI
10.1103/physreva.86.052323

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We investigate the implementation of a measurement for binary optical coherent states that minimizes the error probability with a fixed rate of an inconclusive result. As a special case, the optimal measurement without inconclusive results, which is expressed as a projective measurement, can be implemented using only a beam splitter, a local coherent light source, a photon detector, and a feedback circuit. We find that the optimal measurement for binary optical coherent states with any probability of an inconclusive result can be implemented by the same optical components, even though the measurement is generally not projective.
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We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using nonprobabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver is experimentally demonstrated and compared to an experimental realization of a homodyne receiver with postselection. In the comparison, it becomes clear that the performance of the PNR receiver surpasses the performance of the homodyne receiver, which we prove to be optimal within any Gaussian operations and conditional dynamics.
We consider the problem of discrimination between a set of quantum states with the maximum probability of correct detection for a fixed rate of inconclusive results. We show that this type of measurement can be decomposed into two steps. The first step is the discrimination of whether the measurement result is inconclusive. The second step, which is performed in the case in which a conclusive result was obtained, is minimum error discrimination of output states of the first step. Using this result, we derive a closed-form analytical expression for an optimal measurement for both a geometrically uniform pure-state set and a set of binary doubly symmetric mixed states for any probability of an inconclusive result.