Error Probability Analysis of Quantum Communication with Phase-squeezed M-PSK
For quantum communication researchers, this provides accurate analytical tools for phase-squeezed M-PSK, though the Mark-II receiver is a specific implementation.
The paper analyzes the symbol error probability of phase-squeezed M-PSK using a Mark-II receiver, showing that phase squeezing reduces SEP compared to coherent states, with gains up to nearly doubling photon efficiency for higher constellation orders.
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.