Reconstructing Quantum States from Local Observation: A Dynamical Viewpoint

TL;DR

This paper explores how to reconstruct unknown quantum states in multipartite systems using local measurements and system dynamics, highlighting the importance of dynamics for state reconstruction when static measurements are insufficient.

Contribution

It introduces a system-theoretic observability approach to quantum state reconstruction, emphasizing the role of dynamics in determining states from local observations.

Findings

Reconstruction possible via dynamics even when static measurements are insufficient.

Analysis of how dynamical generators influence reconstructability.

Discussion on finite sample effects and measurement choices.

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.