Entangled random pure states with orthogonal symmetry: exact results

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

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