Decomposition and partial trace of positive matrices with Hermitian blocks

TL;DR

This paper explores how positive semidefinite matrices with Hermitian blocks can be decomposed and related to their partial traces, providing insights relevant to quantum information theory.

Contribution

It introduces a decomposition method for positive matrices with Hermitian blocks, connecting them to their partial traces and deriving related inequalities.

Findings

H can be expressed as an average of isometrically congruent matrices to its partial trace

Provides corollaries related to quantum separability criteria

Enhances understanding of matrix decomposition in quantum information

Abstract

Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important inequalities in quantum information theory such as the Nielsen-Kempe separability criterion.