Electrical Engineering Trailblazer Seminar

Abstract: Quantum hypothesis testing (QHT) has been extensively studied from an information-theoretic perspective, focusing on the optimal decay rate of error probabilities based on the number of samples of an unknown state. First, we examine the sample complexity of QHT, wherein the goal is to determine the minimum samples needed to reach a desired error probability. We show that the sample complexity of symmetric binary QHT depends logarithmically on the inverse error probability and inversely on the negative logarithm of the fidelity. Next, we explore QHT under privacy constraints, quantified by quantum local differential privacy. We develop upper bounds on the contraction coefficients of quantum divergences under privacy constraints, including the hockey-stick divergence, and fully characterize the contraction coefficient for the trace distance. Finally, we derive bounds on the sample complexity of private QHT and identify cases where these bounds are tight.

Joint works with Hao-Chung Cheng, Nilanjana Datta, Nana Liu, Robert Salzmann, and Mark