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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optimal strategy of quantum detection for ASK coherent and PSK squeezed-state signals

Xiaoyu Chen, Peiliang Qiu

Published Oct 3, 2000• 0 citations
Publisher

Abstract

In this paper, we analyze the performance of error probability of amplitude shift keying (ASK) system of coherent state signals and phase shift keying (PSK) system of squeezed state signals, in which we use a quantum receiver called square root measurement.
DOI
10.1117/12.401732

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We analyze the performance of the error probability and the mutual information for quadrature amplitude modulation (QAM) and phase-shift keying systems based on quantum detection theory. It is shown that the quantum receiver called square root measurement gives about 5.7 dB improvement in power in comparison with the classical one. Furthermore, we show that the quantum QAM system can achieve the same reliability as the conventional intensity modulation-direct detection (IM-DD) system with almost equal power, compressing the required bandwidth, while the reliability is degraded in general.
Construction method of an optical receiver is proposed for binary squeezed state signal, which has substantially lower noise properties than a conventional coherent state signal. The receiver can extract most of the performance of a squeezed light. Condition of optimum degree of squeezing are given to the proposed receivers for a binary phase-shift-keyed (BPSK) and an amplitude shift keyed (ASK) signals, respectively. It is also shown that the concept of this receiver can be applied for signals in any other quantum state which is generated from a coherent state by a unitary transformation.
A unified treatment of typical optical modulation formats is given toward a future development of the quantum enigma cipher. In our analysis, the intensity shift keying (ISK), amplitude shift keying (ASK), phase shift keying (PSK), and quadrature amplitude modulation (QAM) coherent state signals are compared in terms of the masking number of potential signals through the numerical calculations of the square-root measurement. Through this comparison, we see that the use of ISK coherent state signal is the best choice for cryptographic purpose among these formats in achieving an appropriate balance between the number of signal photons and the number of quantum state signals.
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.
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.
In this paper, we investigate the symbol error probability (SEP) of phase-squeezed M-ary phase-shift keying (M-PSK). Since the relevant observable for M-PSK detection is the optical phase, we adopt the adaptive Mark-II receiver which is a physically realizable phase measurement. First, we develop a theoretical analysis based on the phase probability operator measure (POM) of the Mark-II scheme in the Fock basis. Then, we develop two SEP methods based on the statistics of the received PSK symbol and the error introduced by the Mark-II measurement. The first method derives the phase probability density induced by the squeezed state noise and incorporates the additional Mark-II phase uncertainty through an angular convolution. Since this convolution does not admit a simple closed form, we also introduce an effective tangential-variance model, which yields a closed form SEP expression in terms of the Owen's T-function. Numerical results show that phase squeezing substantially reduces the SEP of M-PSK compared to coherent state transmission, with greater gains for higher constellation orders. Notably, for the investigated scenario, squeezing can almost double the photon efficiency of M-PSK as the mean number of transmitted photons increases. Finally, the proposed approximations closely follow the Mark-II POM analysis, typically within an accuracy of 2-4 photons, and therefore provide accurate and computationally efficient tools for analyzing phase squeezed quantum M-PSK communication.