Freeness and The Partial Transposes of Wishart Random Matrices

DOI10.4153/CJM-2018-002-2zbMath1462.15037arXiv1706.06711MaRDI QIDQ5378583

James A. Mingo, Mihai Popa

Publication date: 3 June 2019

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.06711

zbMATH Keywords

quantum information theoryrandom matrixWishart matrixfree probabilitypartial transpose

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54) Random matrices (algebraic aspects) (15B52)

Related Items (7)

The partial transpose and asymptotic free independence for Wishart random matrices. II ⋮ On the partial transpose of a Haar unitary matrix ⋮ Asymptotic free independence and entry permutations for Gaussian random matrices ⋮ Asymptotic *-distribution of permuted Haar unitary matrices ⋮ Block-modified Wishart matrices: the easy case ⋮ An asymptotic property of large matrices with identically distributed Boolean independent entries ⋮ Semicircular families of general covariance from Wigner matrices with permuted entries

Cites Work

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• Lectures on the Combinatorics of Free Probability
• Gaussian Hilbert Spaces
• Partial transpose of random quantum states: Exact formulas and meanders
• Real second order freeness and Haar orthogonal matrices

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