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Journal of Russian Laser Research

Receiver Operation Characteristics of Quantum State Discrimination

András Bodor, Mátyás Koniorczyk

Published Mar 1, 2017• 3 citations
Publisher
DOI
10.1007/s10946-017-9629-5

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We provide a description of the problem of the discrimination of two quantum states in terms of receiver operation characteristics analysis, a prevalent approach in classical statistics. Receiveroperation characteristics diagrams provide an expressive representation of the problem, in which quantities such as the fidelity and the trace distance also appear explicitly. In addition we introduce an alternative quantum generalization of the classical Bhattacharyya coefficient. We evaluate our quantum Bhattacharyya coefficient for certain situations and describe some of its properties. These properties make it applicable as another possible quantifier of the similarity of quantum states.
Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing more complex quantum states such as squeezed-displaced states. One of the simplest receivers for state discrimination is the displacement receiver. However, our calculation demonstrates that when we use optimal parameters for a displacement receiver, squeezed-displaced states might not be necessary, and merely using coherent states suffice. We see no performance improvement in terms of probability of error of state discrimination as well as mutual information using displacement receivers when optimal squeezing parameters are used with squeezing operation on the transmitter side for BPSK and QPSK. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using squeezing operation on the receiver side just before detection provides an advantage in terms of increased mutual information for the low-photon regime compared to when no squeezing is used. For all other cases, squeezing offers no additional advantage.
Abstract Quantum state discrimination (QSD) is a fundamental task in quantum information processing with numerous applications. We present a variational quantum algorithm that performs the minimum-error QSD, called the variational quantum state discriminator (VQSD). The VQSD uses a parameterized quantum circuit that is trained by minimizing a cost function derived from the QSD, and finds the optimal positive-operator valued measure (POVM) for distinguishing target quantum states. The VQSD is capable of discriminating even unknown states, eliminating the need for expensive quantum state tomography. Our numerical simulations and comparisons with semidefinite programming demonstrate the effectiveness of the VQSD in finding optimal POVMs for minimum-error QSD of both pure and mixed states. In addition, the VQSD can be utilized as a supervised machine learning algorithm for multi-class classification. The area under the receiver operating characteristic curve obtained in numerical simulations with the Iris flower dataset ranges from 0.97 to 1 with an average of 0.985, demonstrating excellent performance of the VQSD classifier.