Correlation matrices, Clifford algebras, and completely positive semidefinite rank

DOI10.1080/03081087.2018.1529136zbMath1457.15024arXiv1702.06305OpenAlexW2893897940WikidataQ114641378 ScholiaQ114641378MaRDI QIDQ5145555

Anupam Prakash, Antonios Varvitsiotis

Publication date: 21 January 2021

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.06305

zbMATH Keywords

Clifford algebraquantum correlationselliptopecpsd-rank

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Clifford algebras, spinors (15A66) Quantum coherence, entanglement, quantum correlations (81P40) Applications of Clifford algebras to physics, etc. (15A67)

Related Items (1)

Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

Cites Work

• Conic formulations of graph homomorphisms
• Matrices with high completely positive semidefinite rank
• The automorphism group of a completely positive cone and its Lie algebra
• Polynomials with and without determinantal representations
• Hyperbolic polynomials and generalized Clifford algebras
• Positive semidefinite rank
• Extremal correlation matrices
• Non-closure of the set of quantum correlations via graphs
• Completely positive semidefinite rank
• Quantum analogues of the Bell inequalities. The case of two spatially separated domains
• Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla (With an appendix by Narutaka Ozawa)
• On the copositive representation of binary and continuous nonconvex quadratic programs
• New Lower Bounds and Asymptotics for the cp-Rank
• Conic Approach to Quantum Graph Parameters Using Linear Optimization Over the Completely Positive Semidefinite Cone
• Symmetry, Representations, and Invariants
• A Note on Extreme Correlation Matrices
• Completely positive matrices associated withM-matrices
• THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED
• Geometry of cuts and metrics
• Unnamed Item
• Unnamed Item

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