Entangled random pure states with orthogonal symmetry: exact results

2010/06/01 by Pierpaolo Vivo
Computer Science · Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Hilbert space #Probability density function #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Random Matrices and Applications #Random matrix #Random variable #Space (punctuation) #cond-mat.stat-mech #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/43/40/405206

published as J. Phys. A: Math. Theor. 43 (2010) 405206 · 15 pages, 5 figures

arxiv created 2010/06/01 · openalex publication_date 2010/09/15 · arxiv updated 2015/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We compute analytically the density ϱ N , M (λ) of Schmidt eigenvalues, distributed according to a fixed-trace Wishart–Laguerre measure, and the average Rényi entropy for reduced density matrices of entangled random pure states with orthogonal symmetry (β = 1). The results are valid for arbitrary dimensions N = 2 k , M of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.

Citations

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