Journal of Statistical Physics

, Volume 131, Issue 1, pp 33–49 | Cite as

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

  • Satya N. Majumdar
  • Oriol Bohigas
  • Arul Lakshminarayan
Article
First Online:
Received:
Accepted:

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 N strongly correlated random variables for all values of N (and not just for large N).

Keywords

Entanglement Random pure state Extreme value statistics 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Satya N. Majumdar
    • 1
  • Oriol Bohigas
    • 1
  • Arul Lakshminarayan
    • 2
  1. 1.Laboratoire de Physique Théorique et Modèles Statistiques (UMR 8626 du CNRS)Université Paris-SudOrsay CedexFrance
  2. 2.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany

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