Reconstructing Quantum States from Local Observation: A Dynamical Viewpoint

Abstract

We analyze the problem of reconstructing an unknown quantum state of a multipartite system from repeated measurements of local observables. In particular, via a system-theoretic observability analysis, we show that, even when the initial state is not uniquely determined for a static system, this can be reconstructed if we leverage the system's dynamics. The choice of dynamical generators and the effect of finite samples is discussed, along with an illustrative example.

This work has been presented at the Conference on Decision and Control 2024, Milan, Italy. The paper will appear in the conference proceedings