Certifying Quantum Separability with Adaptive Polytopes

TL;DR

This paper introduces an adaptive polytope-based method to certify quantum separability, enabling practical recognition of entanglement properties in small to medium quantum systems and distinguishing various entanglement classes.

Contribution

It presents a novel algorithm using adaptive polytopes for certifying quantum separability and characterizing entanglement in multi-particle systems.

Findings

Conclusive recognition of two-particle separability for small and medium dimensions.

Full separability characterization for up to five qubits or three qutrits.

Identification of maximally robust states with unique entanglement properties.

Abstract

The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum separability of two- and multiparticle quantum systems based on an adaptive polytope approximation. This leads to an algorithm which, for practical purposes, conclusively recognises two-particle separability for small and medium-size dimensions. For multiparticle systems, the approach allows to characterise full separability for up to five qubits or three qutrits; in addition, different classes of entanglement can be distinguished. Finally, our methods allow to identify systematically quantum states with interesting entanglement properties, such as maximally robust states which are separable for all bipartitions, but not fully separable.