Optimally Displaced Threshold Detection for TPSK Modulated Coherent States

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.