Invariance of bipartite separability and PPT-probabilities over Casimir invariants of reduced states

DOI10.1007/s11128-016-1352-6zbMath1348.81111arXiv1512.07210OpenAlexW2342435752MaRDI QIDQ331422

Paul B. Slater

Publication date: 27 October 2016

Published in: Quantum Information Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.07210

zbMATH Keywords

random matrix theoryentanglementpartial transpose\({2\times 3}\) quantum systems\(\mathrm{SU}(3)\)\(\mathrm{SU}(n)\)Bloch radiusBloch vectorcubic Casimir invariantgeneralized Bloch radiiHilbert-Schmidt measurequadratic Casimir invariantqubit-qutritreduced quantum systemsseparability probabilities

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (3)

Master Lovas-Andai and equivalent formulas verifying the \(\frac{8}{33}\) two-qubit Hilbert-Schmidt separability probability and companion rational-valued conjectures ⋮ Extensions of generalized two-qubit separability probability analyses to higher dimensions, additional measures and new methodologies ⋮ Numerical and exact analyses of Bures and Hilbert-Schmidt separability and PPT probabilities

Cites Work

• Unnamed Item
• Formulas for rational-valued separability probabilities of random induced generalized two-qubit states
• On the geometric probability of entangled mixed states
• A fast algorithm for proving terminating hypergeometric identities
• The Bloch vector for \(N\)-level systems
• Interval estimation for a binomial proportion. (With comments and a rejoinder).
• Separability of mixed states: necessary and sufficient conditions.
• \(\mathrm{SU}(6)\) Casimir invariants and \(\mathrm{SU}(2) \otimes \mathrm{SU}(3)\) scalars for a mixed qubit-qutrit state
• Numerical computations of separability probabilities
• On the ring of local polynomial invariants for a pair of entangled qubits
• Induced measures in the space of mixed quantum states
• A concise formula for generalized two-qubit Hilbert–Schmidt separability probabilities
• Moment-based evidence for simple rational-valued Hilbert–Schmidt generic 2 × 2 separability probabilities
• Geometry of the generalized Bloch sphere for qutrits
• On the structure of the body of states with positive partial transpose
• Separability probability formulas and their proofs for generalized two-qubit X-matrices endowed with Hilbert–Schmidt and induced measures
• Bures volume of the set of mixed quantum states
• Hilbert–Schmidt volume of the set of mixed quantum states
• Separability Criterion for Density Matrices
• Matrix models for beta ensembles
• Geometry of density matrix states
• The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group $SL(3,{\mathbb {C}})$
• Volumes of conditioned bipartite state spaces
• Generating random density matrices
• Geometries of quantum states
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
• Dyson indices and Hilbert–Schmidt separability functions and probabilities
• Geometry of Quantum States
• Entanglement Thresholds for Random Induced States

This page was built for publication: Invariance of bipartite separability and PPT-probabilities over Casimir invariants of reduced states