Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State View Full Text


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Article Info

DATE

2008-04

AUTHORS

Satya N. Majumdar, Oriol Bohigas, Arul Lakshminarayan

ABSTRACT

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of Nstrongly correlated random variables for all values of N (and not just for large N). More... »

PAGES

33-49

References to SciGraph publications

  • 1996-04. On orthogonal and symplectic matrix ensembles in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2000-02. Shape Fluctuations and Random Matrices in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2005-05. Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces in JOURNAL OF STATISTICAL PHYSICS
  • 1994-01. Level-spacing distributions and the Airy kernel in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-07. Aspects of Generic Entanglement in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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