Maximal rank of extremal marginal tracial states

TL;DR

This paper investigates the properties and limitations of extremal marginal tracial states in coupled quantum systems, focusing on their maximal rank and special cases like diagonal states.

Contribution

It provides new insights into the maximal rank of extremal marginal tracial states and explores the structure of diagonal marginal tracial states.

Findings

Determined the maximal rank of extremal marginal tracial states.

Characterized diagonal marginal tracial states.

Enhanced understanding of the structure of these quantum states.

Abstract

States on coupled quantum system whose restrictions to each subsystems are normalized traces are called marginal tracial states. We investigate extremal marginal tracial states and maximal rank of such states. Diagonal marginal tracial states are also considered.