Convex politopes and quantum separability

TL;DR

This paper introduces a new geometric approach to quantum entanglement using convex polytopes and the Schlienz-Mahler measure, providing a novel criterion for quantum state separability.

Contribution

It proposes a convex subset-based criterion that generalizes properties of product states, revealing new geometric insights into quantum separability.

Findings

Develops a convex subset criterion for quantum separability

Uncovers a new geometric property of entangled states

Extends the Schlienz-Mahler measure to convex sets

Abstract

We advance a novel perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose an criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum-states) that is able to uncover a new geometrical property of the separability property.