Active Hypothesis Testing for Quantum Detection of Phase-Shift Keying Coherent States

TL;DR

This paper applies active hypothesis testing to quantum detection of phase-shift keying coherent states, deriving error bounds and revealing optimal strategies under resource constraints, advancing quantum communication receiver design.

Contribution

It introduces an active hypothesis testing framework for quantum PSK detection with resource constraints, providing analytical bounds and optimal policies for quantum receiver design.

Findings

Derived upper bounds on Bayesian error probability.

Identified non-trivial optimal policies for high dark counts.

Established a framework for resource-constrained quantum detection analysis.

Abstract

This paper explores the quantum detection of Phase-Shift Keying (PSK)-coded coherent states through the lens of active hypothesis testing, focusing on a Dolinar-like receiver with constraints on displacement amplitude and energy. With coherent state slicing, we formulate the problem as a controlled sensing task in which observation kernels have parameters shrinking with sample size. The constrained open-loop error exponent and a corresponding upper bound on the Bayesian error probability are proven. Surprisingly, the exponent-optimal open-loop policy for binary PSK with high dark counts is not simply time-sharing. This work serves as a first step towards obtaining analytical insights through the active hypothesis testing framework for designing resource-constrained quantum communication receivers.