Geometry of entanglement and separability in Hilbert subspaces of dimension up to three
Liss, Rotem (Institut de Ciències Fotòniques)
Mor, Tal (Technion (Haifa, Israel). Computer Science Department)
Winter, Andreas (Universitat Autònoma de Barcelona. Departament de Física)

Date:	2024
Abstract:	We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In bipartite systems, we characterise the 14 possible qualitatively different geometric shapes for the set of separable states in any three-dimensional Hilbert subspace (5 classes which also appear in two-dimensional subspaces and were found and analysed by Boyer et al. (Phys Rev A 95:032308, 2017. https://doi. org/10. 1103/PhysRevA. 95. 032308), and 9 novel classes which appear only in three-dimensional subspaces), describe their geometries, and provide figures illustrating them. We also generalise these results to characterise the sets of fully separable states (and hence the complementary sets of somewhat entangled states) in three-dimensional subspaces of multipartite systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces.
Grants:	Ministerio de Ciencia e Innovación CEX2019-000910-S Agencia Estatal de Investigación PCI2022-132965 Agencia Estatal de Investigación PID2019-107609GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1127
Note:	Altres ajuts: acords transformatius de la UAB
Note:	Altres ajuts: CERCA Programme/Generalitat de Catalunya; Fundació Cellex; Fundació Mir-Puig
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Quantum entanglement ; Separable states ; Convex geometry
Published in:	Letters in mathematical physics, Vol. 114, Issue 3 (June 2024) , art. 86, ISSN 1573-0530

DOI: 10.1007/s11005-024-01816-w

31 p, 1.8 MB

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