Sample Complexity of Locally Differentially Private Quantum Hypothesis Testing

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.
Comment: 24 pages. Short version accepted at ISIT 2024. This work is independent and concurrent to "Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing" by Theshani Nuradha and Mark M. Wilde