Optimally Displaced Threshold Detection for Discriminating Binary Coherent States Using Imperfect Devices

TL;DR

This paper analytically evaluates the performance of an optimized displaced threshold detection method for binary coherent state discrimination using a generalized Kennedy receiver, considering realistic noise and device imperfections.

Contribution

It introduces a heuristic greedy search algorithm to find optimal thresholds and displacements, improving discrimination performance under practical conditions.

Findings

Optimal threshold and displacement are analytically characterized.

The proposed algorithm achieves lower error probabilities than existing methods.

ODTD reduces to Kennedy receiver with threshold detection at high signal powers.

Abstract

Because of the potential applications in quantum information processing tasks, discrimination of binary coherent states using generalized Kennedy receiver with maximum a posteriori probability (MAP) detection has attracted increasing attentions in recent years. In this paper, we analytically study the performance of the generalized Kennedy receiver having optimally displaced threshold detection (ODTD) in a realistic situation with noises and imperfect devices. We first prove that the MAP detection for a generalized Kennedy receiver is equivalent to a threshold detection in this realistic situation. Then we analyze the properties of the optimum threshold and the optimum displacement for ODTD, and propose a heuristic greedy search algorithm to obtain them. We prove that the ODTD degenerates to the Kennedy receiver with threshold detection when the signal power is large, and we also clarify the connection between the generalized Kennedy receiver with threshold detection and the one-port homodyne detection. Numerical results show that the proposed heuristic greedy search algorithm can obtain a lower and smoother error probability than the existing works.