Partial transpose of random quantum states: Exact formulas and meanders

DOI10.1063/1.4799440zbMath1285.81005arXiv1211.1525OpenAlexW3104401626MaRDI QIDQ5397804

Piotr Śniady, Motohisa Fukuda

Publication date: 24 February 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.1525

zbMATH Keywords

normalized trace class operators

Mathematics Subject Classification ID

Random matrices (algebraic aspects) (15B52) Quantum coherence, entanglement, quantum correlations (81P40) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (11)

On the separability of unitarily invariant random quantum states: the unbalanced regime ⋮ The partial transpose and asymptotic free independence for Wishart random matrices. II ⋮ On the reduction criterion for random quantum states ⋮ Freeness and The Partial Transposes of Wishart Random Matrices ⋮ Block-modified Wishart matrices: the easy case ⋮ Random matrix techniques in quantum information theory ⋮ On the asymptotic distribution of block-modified random matrices ⋮ Quantum groups, from a functional analysis perspective ⋮ Holographic entanglement negativity and replica symmetry breaking ⋮ Negativity spectra in random tensor networks and holography ⋮ Additivity rates and PPT property for random quantum channels

Cites Work

• Asymptotic eigenvalue distributions of block-transposed Wishart matrices
• Hastings's additivity counterexample via Dvoretzky's theorem
• Meander, folding, and arch statistics
• Some properties of crossings and partitions
• Random matrices with complex Gaussian entries
• The Euler characteristic of the moduli space of curves
• Separability of mixed states: necessary and sufficient conditions.
• Asymptotics of random density matrices
• Induced measures in the space of mixed quantum states
• PARTIAL TRANSPOSITION OF RANDOM STATES AND NON-CENTERED SEMICIRCULAR DISTRIBUTIONS
• Lectures on the Combinatorics of Free Probability
• Separability Criterion for Density Matrices

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