Separability Criterion for Density Matrices

Phys. Rev. Lett. 77, 1413 – Published 19 August 1996
Asher Peres


A quantum system consisting of two subsystems is separable if its density matrix can be written as ρ=ΣA wAρAρA, where ρA and ρA are density matrices for the two subsystems, and the positive weights wA satisfy ΣwA=1. In this Letter, it is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of ρ, has only non-negative eigenvalues. Some examples show that this criterion is more sensitive than Bell's inequality for detecting quantum inseparability.


  • Received 8 April 1996
  • Published in the issue dated 19 August 1996

© 1996 The American Physical Society

Authors & Affiliations

Asher Peres

  • Department of Physics, Technion–Israel Institute of Technology, 32 000, Haifa, Israel

References (Subscription Required)

Authorization Required




Log In



Article Lookup
Paste a citation or DOI

Enter a citation
  1. Enter a citation to look up or terms to search.

    Ex: "PRL 112 068103", "Phys. Rev. Lett. 112, 068103", "10.1103/PhysRevLett.112.068103"