Coherent-state multiple-symbol detection scheme for underwater quantum communications impaired by turbulence fading

Coherent states are increasingly being adopted for transmitting information in underwater quantum communications (UQCs). This paper presents what we believe to be a novel quantum multiple-symbol detection (QMSD) scheme designed to alleviate the performance degradation present in classical quantum symbol-by-symbol detection schemes, while operating without the need for channel state information (CSI) at the receiver. We model the communication system under the influence of an underwater channel and thermal noise at the receiver, and propose a novel QMSD metric based on positive operator-valued measure (POVM) quantum measurement results. Furthermore, we derive a closed-form expression for the QMSD metric for facilitating easy evaluation under marine turbulence conditions and thereby reducing implementation complexity. Using the simplified QMSD metric, we employ a sliding window algorithm to efficiently process the received quantum symbol sequence. Simulation results demonstrate that our proposed QMSD scheme enhances the quality of UQCs and exhibits robustness under marine turbulence conditions. Specifically, as the length of the detection sequence increases, the error probability of our scheme decreases. Moreover, as the average number of transmitted photons increases, the proposed QMSD scheme demonstrates superior performance, reducing error probability by 3 orders of magnitude compared to the quantum maximum likelihood detection (QMLD) scheme and by 5 orders of magnitude relative to the traditional homodyne detection (HD) scheme.