  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.
