Error Probability Analysis of Quantum Communication with Phase-squeezed M-PSK

2026-06-11

AI Summary

This work addresses the high symbol error probability (SEP) in high-order M-ary phase-shift keying (M-PSK) quantum communication using coherent states by introducing phase-squeezed states into M-PSK modulation for the first time. Building upon the physically realizable phase measurement of the Mark-II receiver, the authors model the phase probability operator measure (POM) in the Fock basis, incorporating both squeezing-induced noise and measurement uncertainty. By employing angular convolution and a tangential variance approximation, they derive a closed-form SEP approximation expressed via Owen’s T function. The resulting model achieves significant computational efficiency—introducing only 2–4 photon-equivalent errors—and reveals that phase squeezing can nearly double photon efficiency, substantially reducing SEP especially for high-order constellations.

Abstract

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.

Problem

• symbol error probability
• phase-squeezed M-PSK
• quantum communication
• phase measurement
• optical phase

Innovation

• phase squeezing
• M-PSK
• symbol error probability
• Mark-II receiver
• Owen's T-function