On the mixed UDA states and additivity

TL;DR

This paper characterizes when multipartite mixed quantum states are uniquely determined by their reduced states, providing systematic methods and insights into their additivity, with applications in quantum tomography.

Contribution

It establishes necessary and sufficient conditions for UDA states based on reduced density matrices and characterizes their additivity properties.

Findings

Complete characterization of UDA bipartite states

Systematic method for identifying UDA states

Application insights for quantum tomography

Abstract

Mixed states that are uniquely determined among all (UDA) states are vital in efficient quantum tomography. We show the necessary and sufficient conditions by which some multipartite mixed states are UDA by their $k$-partite reduced density matrices. The case for $k=2$ is mostly studied, which requires minimal local information and shows practical benefits. Based on that, we establish a systematic method for determining UDA states and provide a complete characterization of the additivity of UDA bipartite and three-qubit product states. We show the application of mixed UDA states and their characterization from the perspectives of tomography and other tasks.