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.

翻译：量子态区分是众多信息处理任务中的一个重要问题。本文旨在研究当量子态经过一个需要满足局部差分隐私的量子信道预处理时，该问题可能达到的最佳样本复杂度。为此，我们针对不同设置给出了可达性界与逆界。这包括多种机制下的对称态区分以及非对称情形。在研究过程中，我们还证明了无约束一般情形下的新样本复杂度界。实现这一目标的重要工具是我们提出的新熵不等式，我们相信这些不等式本身也具有独立的研究价值。