Sample Complexity of Locally Differentially Private Quantum Hypothesis Testing

TL;DR

This paper investigates the minimum number of quantum samples needed for state discrimination under local differential privacy constraints, providing bounds and new entropy inequalities for various scenarios.

Contribution

It introduces the first bounds on sample complexity for locally differentially private quantum hypothesis testing, including symmetric and asymmetric cases, with new entropy inequalities.

Findings

Achievability and converse bounds for different quantum state discrimination settings.

New entropy inequalities relevant to quantum information theory.

Improved understanding of sample complexity under privacy constraints.

Abstract

Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required to be locally differentially private. To that end we provide achievability and converse bounds for different settings. This includes symmetric state discrimination in various regimes and the asymmetric case. On the way, we also prove new sample complexity bounds for the general unconstrained setting. An important tool in this endeavor are new entropy inequalities that we believe to be of independent interest.