Channel-state duality and the separability problem

TL;DR

This paper explores the separability of quantum states using the Choi-Jamiolkowski isomorphism, deriving spectral criteria and providing examples including a separable decomposition of 2x2 isotropic states.

Contribution

It introduces a novel approach linking channel-state duality to the separability problem, offering new spectral criteria and explicit decompositions.

Findings

Spectral separability criteria derived

Separable decomposition of 2x2 isotropic states obtained

Illustrative examples demonstrating the approach

Abstract

Separability of quantum states is analyzed with the use of the Choi-Jamiolkowski isomorphism. Spectral separability criteria are derived. The presented approach is illustrated with various examples, among which a separable decomposition of 2 \otimes 2 isotropic states is obtained.