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

2025-01-27

AI Summary

Quantum detection of phase-shift-keying (PSK) coherent-state signals under resource constraints—such as high dark-count rates and energy/amplitude limitations—remains challenging due to fundamental quantum noise and operational restrictions. Method: We propose a Dolinar-like receiver optimization framework grounded in active hypothesis testing, modeling the reception process as a controlled Markov decision process. We introduce coherent-state slicing and a contraction-type observation kernel to enable analytical performance characterization within this paradigm. Contribution/Results: We establish that, under high dark-count conditions, the exponentially optimal open-loop strategy for binary PSK is not the conventional time-division scheme—contradicting prevailing intuition. We rigorously derive tight bounds on the open-loop error exponent and the Bayesian error probability under energy/amplitude constraints. This work provides the first analytical foundation and fundamental performance limits for quantum receivers operating under realistic resource constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Quantum Communication
• Resource-constrained Optimization
• Active Hypothesis Testing

Innovation

• Active Hypothesis Testing
• Coherent State Slicing
• Bayesian Error Probability Bound