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Typical entanglement

  • Fabio Deelan Cunden
  • Paolo Facchi
  • Giuseppe Florio
  • Saverio PascazioEmail author
Review

Abstract

Let a pure state |ψ〉 be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix ρ A of an N-dimensional subsystem. The bipartite entanglement properties of |ψ〉 are encoded in the spectrum of ρ A . By means of a saddle point method and using a “Coulomb gas” model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function.

Keywords

Partition Function Lagrange Multiplier Pure State Saddle Point Method Reduce Density Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fabio Deelan Cunden
    • 1
  • Paolo Facchi
    • 2
    • 3
  • Giuseppe Florio
    • 4
    • 2
    • 3
  • Saverio Pascazio
    • 2
    • 3
    Email author
  1. 1.Dipartimento di MatematicaUniversità di BariBariItaly
  2. 2.Dipartimento di Fisica and MECENASUniversità di BariBariItaly
  3. 3.Sezione di BariINFNBariItaly
  4. 4.Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”RomaItaly

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