Abstract: Quantum hypothesis testing for states has traditionally been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown state. As such, these studies mainly focused on the asymptotic setting (n → ∞). However, in practice, the regime of interest involves access to finite number of samples. In this talk, I will introduce the sample complexity of quantum hypothesis testing, wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. We characterize the optimal sample complexity of quantum hypothesis testing. In fact, for sufficiently small error probability, our upper and lower bounds on sample complexity differ only by a constant factor of four. Next, I will discuss the sample complexity of hypothesis testing when you have access to noisy and privatized quantum states instead of noiseless quantum states. Towards this, I will introduce quantum local differential privacy and characterize the cost one need to pay to ensure privacy.
Bio: Theshani Nuradha is a J.L. Doob Research Assistant Professor in the Department of Mathematics and an IQUIST Postdoctoral Scholar, working on quantum information theory and mentored by Prof. Felix Leditzky.