Decomposition and partial trace of positive matrices with Hermitian blocks

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.

References in corpus (2)

• Separable states are more disordered globally than locally
• A matrix realignment method for recognizing entanglement