Certifying Quantum Separability with Adaptive Polytopes

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.

Submission to SciPost, 9 + 12p pages, 8 figures

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Cited by in corpus (6)

• Semidefinite programming relaxations for quantum correlations
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• Geometry of two-body correlations in three-qubit states
• Entanglement Superactivation in Multiphoton Distillation Networks
• Certifying the activation of Bell nonlocality with finite data