Adversarial Hypothesis Testing for Quantum Channels

2026-01-15

AI Summary

This study addresses the problem of hypothesis testing between quantum-quantum (QQ) and classical-quantum (CQ) channels in an adversarial setting, where the sender, Alice, chooses inputs in the worst possible manner to impair the receiver Bob’s ability to distinguish between the channels. By developing a unified framework for adversarial channel discrimination, the work systematically characterizes the fundamental limits of distinguishability across four scenarios—determined by whether Alice employs independent and identically distributed or general input strategies, and whether Bob has prior knowledge of the inputs. The analysis leverages tools from quantum information theory and Stein’s lemma, with explicit comparisons between entangled and separable input strategies. A key finding is that CQ channels are not merely a special case of QQ channels: while Bob’s advantage from prior knowledge vanishes under general inputs for QQ channels, it persists for CQ channels, revealing a fundamental distinction between the two channel types in adversarial hypothesis testing.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Quantum Machine Learning
• Search and Optimization: Adversarial Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects the channel input adversarially to minimize Bob's distinguishability. We analyze this problem across four settings based on whether Alice employs i.i.d. or general inputs and whether the receiver, Bob, is informed of the specific input choice (allowing his measurement to depend on the input). We characterize the Stein exponents for each setting and reveal a striking distinction in behavior: for QQ channels with i.i.d. inputs, Bob's knowledge of the input significantly enhances distinguishability, yet this advantage vanishes when general inputs are permitted. In contrast, for CQ channels, Bob being informed provides a consistent advantage over the corresponding entanglement-breaking channels for both i.i.d. and general inputs. These results demonstrate a unique phenomenon in adversarial hypothesis testing where the CQ channel does not merely behave as a special case of the QQ channel.

Problem

• adversarial hypothesis testing
• quantum channels
• channel discrimination
• classical-quantum channels
• quantum-quantum channels

Innovation

• adversarial hypothesis testing
• quantum channels
• Stein exponent
• classical-quantum channels
• channel discrimination