Journal article
The joint distribution of the marginals of multipartite random quantum states
Stephane Dartois, Luca Lionni, Ion Nechita
RANDOM MATRICES-THEORY AND APPLICATIONS | WORLD SCI PUBL CO INC | Published : 2020
Abstract
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.
Grants
Awarded by Australian Research Council
Awarded by ANR project StoQ
Awarded by ANR project NEXT
Awarded by PHC Sakura program
Funding Acknowledgements
L.L. is a JSPS International Research Fellow. The work of S.D. was partially supported by the Australian Research Council grant DP170102028. I.N.'s research has been supported by the ANR projects StoQ (grant number ANR-14-CE25-0003-01) and NEXT (grant number ANR-10-LABX-0037-NEXT), and by the PHC Sakura program (grant number 38615VA). I.N. also acknowledges the hospitality of the Technische Universitat Munchen. The authors would like to thank the Institut Henri Poincar ' e in Paris for its hospitality and for hosting the trimester on "Analysis in Quantum Information Theory", during which part of this work was undertaken. S.D. and I.N. would also like to thank the organizers of the "QUATR-17" conference in Skoltech/Moscow, and especially Leonid Chekhov, for bringing together researchers in random tensor theory and quantum information theory.