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Journal of Optics B Quantum and Semiclassical Optics

Optimal signal detection in entanglement-assisted quantum communication systems

Masashi Ban

Published Mar 1, 2002• 4 citations
Publisher

Abstract

Minimization of error probability is considered in entanglement-assisted quantum communication systems. It is shown that although quantum state signals being sent are not symmetric at a sender side, the square root measurement becomes optimum when they are made symmetric at the receiver side. For communication systems of coherent signals, where a two-mode squeezed-vacuum state is used as an entanglement resource, the quantum entanglement greatly reduces the average probability of error. The relation to the quantum dense coding of continuous variables is also discussed.

DOI
10.1088/1464-4266/4/2/310

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Minimization of error probability is considered in entanglement-assisted quantum communication systems. It is shown that although quantum state signals being sent are not symmetric at a sender side, the square root measurement becomes optimum when they are made symmetric at the receiver side. For communication systems of coherent signals, where a two-mode squeezed-vacuum state is used as an entanglement resource, the quantum entanglement greatly reduces the average probability of error. The relation to the quantum dense coding of continuous variables is also discussed.
The possibility is explicitly shown that the average probability of error is reduced and the transmission rate of information is enhanced by means of entangled input states to a communication channel. When two senders transmit some information to a receiver, they encode the information in the quadrature amplitudes of both modes of a two-mode squeezed vacuum state. The receiver performs a simultaneous measurement of the two quadrature amplitudes of the received two-mode state. In this case, if the average value of the photon number supplied to the communication system is not so small, the average probability of error becomes smaller than that of the communication system without entanglement. Furthermore, the transmission rate of information becomes larger than the quantum capacity of classical information of the communication system without entanglement.
An important problem in quantum information theory is finding the best possible performance of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. 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 a number of quantum states such as coherent states and squeezed-displaced states. In this thesis, we provide optimal receiver design employing coherent states and squeezed-displaced states to maximize the mutual information and lower the error probability of state discrimination. In the case of pure coherent states, we derive an alternative channel capacity of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that the capacity is higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacements. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. We also explore the use of squeezing operations with a displacement receiver for state discrimination. Our calculation demonstrates that we see no performance improvement in terms of the probability of error of state discrimination or mutual information using displacement receivers when optimal squeezing on the transmitter side is used. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using the squeezing operation on the receiver side provides an advantage in terms of increased mutual information for the low-photon number regime compared to when no squeezing is used. In the later part of the thesis, we study entanglement-assisted communication using two-mode squeezing vacuum. The use of pre-shared entanglement in entanglement-assisted communication provides a superior alternative to classical communication specifically in the low brightness regime and highly noisy environment. In this thesis, we analyze the performance of a few low-complexity receivers that employ optical parametric amplifiers. In the simulation, we demonstrate that receiver designs with an entanglement-assisted scheme using phase-shift-keying modulation can outperform classical capacities. We describe a newly proposed 2x2 optical hybrid receiver for entanglement-assisted communication whose performance is roughly 10% better in terms of error probability as compared to previously proposed optical parametric amplifier-based receivers. Further, we find that using unequal priors for BPSK provides approximately three times the advantage over equal priors in terms of information rate.
Quantum dense coding of continuous variables via a two-mode squeezed vacuum state is considered for a noisy quantum channel. Classical information is encoded in the two quadrature components of one mode of a two-mode squeezed vacuum state and the encoded mode is sent through a noisy quantum channel which is assumed to be linearly dissipative. Decoding at the receiver side is performed by simultaneous measurement of two quadrature components of the two-mode state. By calculating the error probability of a binary communication system, we examine whether the dense coding is effective or not when a quantum channel is noisy.
The calculation method proposed here obtains an optimum detection process for an M-ary signal whose quantum states are linearly independent and nonorthogonal. Optimizations are carried out by minimizing the average probability of error or by maximizing the mutual information in the signal detection process. Quantum detection operators, in terms of which the signal detection process is mathematically described, are assumed to be projection operators defined on a Hilbert space H s spanned by the quantum states of the signal; that is, the best projection operators that describe the signal detection process are obtained. The optimization procedure is equivalent to finding an appropriate unitary transformation in the Hilbert space H s. For a binary quantum state signal, the optimum detection processes in which the average probability of error is minimized and in which the mutual information is maximized are obtained. It is found that the optimum detection process minimizing the average probability of error is the same as that maximizing the mutual information.