Some New Results in Quantum State Learning

In quantum state learning, one is given samples from a quantum state, and the goal is to output an estimate which is close to the quantum state. Quantum state learning is a fundamental problem in both theory and practice, and the last 10 years have seen substantial progress in the design of sample-optimal algorithms for this task.

In this talk, I will give a survey of recent results in this area, with a focus on a recent set of unbiased estimators for quantum state learning which I have developed with my collaborators. These unbiased estimators have allowed us to give a unified and conceptually simpler framework for achieving optimal sample complexities for a number of important quantum state learning applications.

Based on joint work with Angelos Pelecanos, Thilo Scharnhorst, Jack Spilecki, Ewin Tang, and Mark Zhandry.