IEEE Transactions on Communications

Optimally Displaced Threshold Detection for TPSK Modulated Coherent States

Mufei Zhao, Renzhi Yuan, Chen Feng, Shuai Han, Julian Cheng

Published Aug 29, 2023• 3 citations

Abstract

In this paper, the performance of optimally displaced threshold detection (ODTD) for discriminating ternary coherent signals is theoretically investigated. We first establish the receiver model for ternary phase shift keying optical quantum communication system using Kennedy receiver with ODTD in a realistic situation. Then we analytically study the error probability for ODTD and formulate a joint optimization problem to minimize this error probability of detection, which is a challenging mixed-integer programming (MIP) problem due to the discreteness of the detection threshold. We then propose an efficient algorithm to tackle this MIP problem and design the displacement and the threshold on both detection branches. We also discuss the receiving scheme using ODTD in the case of unequal prior probabilities and optimize the signal power distribution between the two branches. Numerical results show that for the discrimination of ternary coherent signals using Kennedy-type receiver, ODTD can mitigate the influence of thermal noise and dark count noise and is robust to imperfect quantum efficiency. Besides, we find that the error probability performance can be improved by optimizing the decoding order of the ternary signals and the reflectance of the beam splitter.

DOI: 10.1109/tcomm.2023.3309828

Related papers

Optimally Displaced Threshold Detection for Discriminating Binary Coherent States Using Imperfect Devices

Renzhi Yuan, Mufei Zhao, Shuai Han +1 more

Because of the potential applications in quantum information processing tasks, discrimination of binary coherent states using generalized Kennedy receiver with maximum a posteriori probability (MAP) detection has attracted increasing attentions in recent years. In this paper, we analytically study the performance of the generalized Kennedy receiver having optimally displaced threshold detection (ODTD) in a realistic situation with noises and imperfect devices. We first prove that the MAP detection for a generalized Kennedy receiver is equivalent to a threshold detection in this realistic situation. Then we analyze the properties of the optimum threshold and the optimum displacement for ODTD, and propose a heuristic greedy search algorithm to design these parameters. We prove that the ODTD asymptotically approaches the Kennedy receiver with threshold detection when the signal power is large, and we also clarify the connection between the generalized Kennedy receiver with threshold detection and the one-port homodyne detection. Numerical results show that the proposed heuristic greedy search algorithm can obtain a lower and smoother error probability than the existing methods.

arXiv:2007.11109IEEE Transactions on CommunicationsDec 31, 202018 citations

A robust quantum receiver for phase shift keyed signals

C R Müller, Ch Marquardt

The impossibility of perfectly discriminating non-orthogonal quantum states imposes far-reaching consequences both on quantum and classical communication schemes. We propose and numerically analyze an optimized quantum receiver for the discrimination of phase encoded signals. Our scheme outperforms the standard quantum limit and approaches the Helstrom bound for any signal power. The discrimination is performed via an optimized, feedback-mediated displacement prior to a photon counting detector. We provide a detailed analysis of the influence of excess noise and technical imperfections on the average error probability. The results demonstrate the receiver's robustness and show that it can outperform any classical receiver over a wide range of realistic parameters.

arXiv:1412.6242New Journal of PhysicsMar 27, 201546 citations

Displacement receiver for phase-shift-keyed coherent states

Shuro Izumi, Masahiro Takeoka, Mikio Fujiwara +4 more

The quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase-shift-keying coherent states in terms of average error rate and mutual information. Our receiver consists of on-off--type photon detectors and displacement operations without electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently available technology. For the quaternary signals feedforward operation is crucial to overcome the SQL with imperfect devices. We also analytically examine the asymptotic limit of the performance of the proposed receiver with respect to the number of feedforward steps.

arXiv:1208.1815Physical Review AOct 22, 201276 citations

A robust quantum receiver for phase shift keyed signals

Müller, Christian R., Christoph Marquardt

The impossibility of perfectly discriminating non-orthogonal quantum states imposes far-reaching consequences both on quantum and classical communication schemes.Wepropose and numerically analyze an optimized quantum receiver for the discrimination of phase encoded signals. Our scheme outperforms the standard quantum limit and approaches the Helstrom bound for any signal power. The discrimination is performed via an optimized, feedback-mediated displacement prior to a photon counting detector.Weprovide a detailed analysis of the influence of excess noise and technical imperfections on the average error probability. The results demonstrate the receiver’s robustness and show that it can outperform any classical receiver over a wide range of realistic parameters.

Jan 1, 201521 citations

Security of Coherent-State Quantum Key Distribution Using Displacement Receiver

Mufei Zhao, Renzhi Yuan, Chen Feng +2 more

Continuous variable quantum key distribution (CV-QKD) protocol has drawn much attention due to its compatibility with existing optical communication systems. In this paper, we propose a quaternary modulated CV-QKD protocol using displacement receivers and adopt the post-selection scheme to overcome the ‘3dB limit’. We first establish the model of displacement receiver for discriminating quaternary modulated coherent signals in a realistic situation. The performance of non-adaptive displacement receiver and multi-stage feedforward receiver are both investigated under different noises and device imperfections. To improve the receiver performance, we numerically optimize the displacement operation and check the quantum advantage of the displacement receivers over the classical homodyne detection. Then we analyze the security of the proposed CV-QKD protocol. The secret key rate is derived for both types of displacement receivers under the collective beam splitting attack. We also optimize the transmitted signal photons for different channel transmission efficiencies under practical system constraints. Numerical results shed light on the practical application of displacement receivers in CV-QKD protocols. This includes evaluating the necessity of optimizing the displacement and incorporating the feedforward structure in a displacement receiver according to different practical system limitations. Moreover, under higher channel transmission efficiency and increased receiver noise level, a larger coherent amplitude is required for transmitting signals to attain the maximum secret key rate.

IEEE Journal on Selected Areas in CommunicationsMar 22, 20247 citations

Optimized Squeezing Operation for Phase-Shift Keying Quantum State Discrimination

Rahul Kumar Bhadani, Ivan B. Djordjević

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.

IEEE AccessJan 1, 20221 citation