Quantum state tomography via reduced density matrices

TL;DR

This paper explores the limits of quantum state tomography using reduced density matrices, identifying classes of states that are uniquely determined by local measurements under certain assumptions, and experimentally validating these findings.

Contribution

It introduces a new classification of quantum states based on their unique determination by local RDMs, considering the assumption of purity, and experimentally tests the tomography process for these classes.

Findings

States can be uniquely determined by RDMs if the global state is pure.

Some states are not UD without the purity assumption.

Experimental validation shows feasibility and stability of local RDM-based tomography.

Abstract

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.