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.

翻译：本文研究了相位压缩M进制相移键控（M-PSK）的符号错误概率（SEP）。由于M-PSK检测的相关可观测量是光相位，我们采用物理可实现的自适应Mark-II接收机进行相位测量。首先，我们基于Fock基下Mark-II方案的相位概率算符测量（POM）建立了理论分析。随后，我们利用接收PSK符号的统计特性以及Mark-II测量引入的误差，开发了两种SEP计算方法。第一种方法推导了由压缩态噪声引起的相位概率密度，并通过角度卷积将Mark-II附加相位不确定性纳入考量。由于该卷积难以获得简洁的闭合表达式，我们还引入了一种有效切向方差模型，该模型用Owen's T函数给出了闭合形式的SEP表达式。数值结果表明，与相干态传输相比，相位压缩可大幅降低M-PSK的SEP，且对于更高阶星座图可获得更显著的增益。值得注意的是，在所研究的场景中，随着平均传输光子数的增加，压缩几乎能使M-PSK的光子效率翻倍。最后，所提出的近似方法紧密贴合Mark-II POM分析结果（典型精度在2-4光子范围内），因此为分析相位压缩量子M-PSK通信提供了准确且高效的计算工具。