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Article Dans Une Revue Random Matrices: Theory and Applications Année : 2020

The joint distribution of the marginals of multipartite random quantum states

Résumé

We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the marginals are asymptotically free. We connect the matrix integrals relevant to the study of operators on tensor product spaces with the corresponding classes of combinatorial maps, for which we develop the combinatorial machinery necessary for the asymptotic study. Finally, we present some applications to the theory of random quantum states in quantum information theory.
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Dates et versions

hal-02955388 , version 1 (01-10-2020)

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Stephane Dartois, Luca Lionni, Ion Nechita. The joint distribution of the marginals of multipartite random quantum states. Random Matrices: Theory and Applications, 2020, 09 (03), pp.2050010. ⟨10.1142/S2010326320500100⟩. ⟨hal-02955388⟩
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