Separability probability formulas and their proofs for generalized two-qubit X-matrices endowed with Hilbert–Schmidt and induced measures

DOI10.1142/S2010326315500185zbMath1330.15041arXiv1501.02289OpenAlexW1849630064WikidataQ113775130 ScholiaQ113775130MaRDI QIDQ3459158

Charles F. Dunkl, Paul B. Slater

Publication date: 30 December 2015

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.02289

zbMATH Keywords

positive partial transposeHilbert-Schmidt measureseparability probabilitiesinduced measure\(X\)-states\(2\times 2\) quantum systemscontinuous Dyson indexentanglement probability distributionPeres-Horodecki conditions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Random matrices (algebraic aspects) (15B52) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (7)

Formulas for rational-valued separability probabilities of random induced generalized two-qubit states ⋮ Invariance of bipartite separability and PPT-probabilities over Casimir invariants of reduced states ⋮ Master Lovas-Andai and equivalent formulas verifying the \(\frac{8}{33}\) two-qubit Hilbert-Schmidt separability probability and companion rational-valued conjectures ⋮ Further double sums of Dunkl and Gasper ⋮ Extensions of generalized two-qubit separability probability analyses to higher dimensions, additional measures and new methodologies ⋮ Report from the open problems session at OPSFA13 ⋮ Numerical and exact analyses of Bures and Hilbert-Schmidt separability and PPT probabilities

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Formulas for rational-valued separability probabilities of random induced generalized two-qubit states
• Entanglement universality of two-qubit X-states
• Induced measures in the space of mixed quantum states
• Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities
• Hilbert–Schmidt volume of the set of mixed quantum states
• Separability Criterion for Density Matrices
• Matrix models for beta ensembles
• Volumes of conditioned bipartite state spaces
• Geometry of Quantum States
• Entanglement Thresholds for Random Induced States
• Separability of \(n\)-particle mixed states: necessary and sufficient conditions in terms of linear maps

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