Adversarial Hypothesis Testing for Quantum Channels

TL;DR

This paper investigates adversarial hypothesis testing for quantum channels, revealing how input knowledge impacts distinguishability differently for QQ and CQ channels across various input strategies.

Contribution

It provides a comprehensive characterization of Stein exponents in adversarial quantum channel discrimination, highlighting novel distinctions between QQ and CQ channels.

Findings

Input knowledge enhances distinguishability for QQ channels with i.i.d. inputs.

The advantage of input knowledge disappears for QQ channels with general inputs.

For CQ channels, input knowledge consistently improves distinguishability regardless of input type.

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.