Entangled random pure states with orthogonal symmetry: exact results

Abstract

We compute analytically the density ${\varrho }_{N,M}(\lambda )$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average Rényi entropy $⟨{\mathcal{S}}_q⟩$ for reduced density matrices of entangled random pure states with orthogonal symmetry $(\beta =1)$. The results are valid for arbitrary dimensions $N=2k,M$ of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.

15 pages, 5 figures

References in corpus (3)

• Entanglement of random vectors
• Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
• Distribution of G-concurrence of random pure states

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