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Freeness and The Partial Transposes of Wishart Random Matrices

  • James A. Mingo,
    Department of Mathematics and Statistics, Queen’s University , Jeffery Hall, Kingston, Ontario K7L 3N6
  • Mihai Popa,
    Department of Mathematics, The University of Texas at San Antonio , One UTSA Circle, San Antonio, TX 78249, USA
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Abstract

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 a example where the partial transpose produces freeness at the operator level. Finally we investigate the case of real Wishart matrices.
Keywords: free probability, random matrix, partial transpose, quantum information theory free probability, random matrix, partial transpose, quantum information theory
MSC Classifications: 15B52, 46L54, 60B20 show english descriptions Random matrices
Free probability and free operator algebras
Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
15B52 - Random matrices
46L54 - Free probability and free operator algebras
60B20 - Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
 

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