Geodesic
Freeness and The Partial Transposes of Wishart Random Matrices
Canadian journal of mathematics, Tome 71 (2019) no. 3, pp. 659-681

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We show that the partial transposes of complex Wishart random matrices are asymptotically free. We also investigate regimes where the number of blocks is fixed but the size of the blocks increases. This gives an example where the partial transpose produces freeness at the operator level. Finally, we investigate the case of real Wishart matrices.
DOI : 10.4153/CJM-2018-002-2
Mots-clés : free probability, random matrix, partial transpose, quantum information theory 
Mingo, James A.; Popa, Mihai. Freeness and The Partial Transposes of Wishart Random Matrices. Canadian journal of mathematics, Tome 71 (2019) no. 3, pp. 659-681. doi: 10.4153/CJM-2018-002-2
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     author = {Mingo, James A. and Popa, Mihai},
     title = {Freeness and {The} {Partial} {Transposes} of {Wishart} {Random} {Matrices}},
     journal = {Canadian journal of mathematics},
     pages = {659--681},
     year = {2019},
     volume = {71},
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     doi = {10.4153/CJM-2018-002-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-002-2/}
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