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Sample Complexity of Locally Differentially Private Quantum Hypothesis Testing

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arxiv 2406.18658 v1 pith:CVWK5N6V submitted 2024-06-26 quant-ph cs.ITmath.IT

Hao-Chung Cheng , Christoph Hirche , Cambyse Rouzé This is my paper · ORCID
classification quant-phcs.ITmath.IT
keywords complexityquantumsampleboundsdifferentiallydiscriminationimportantlocally
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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.

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  1. Divergence Inequalities with Applications in Ergodic Theory

    cs.IT 2024-11 conditional novelty 5.0 of 10

    For a wide class of f-divergences, asymptotic Markov chain contraction rates are characterized by the input-dependent chi-squared contraction coefficient, and the result extends to Petz f-divergences in quantum settings.

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