國立清華大學 數學系

Abstract：
Quantum state tomography refers to the task of estimating the quantum state of an unknown quantum system from measurement outcomes. It is essential both for verifying the correctness of quantum computing units and for extracting information from quantum computations. This talk focuses on quantum state tomography under the logarithmic loss. In the batch setting, this corresponds to maximum-likelihood quantum state tomography; in the online setting, it gives rise to a non-commutative generalization of online portfolio selection, a classical open problem in online learning theory.
The logarithmic loss introduces significant analytical challenges: It is not globally Lipschitz, nor does it have a Lipschitz gradient, so standard arguments in optimization and learning theory do not directly apply. In this talk, I will present our recent results on batch and online algorithms for quantum state tomography under the logarithmic loss, along with some applications and open problems.