Generalized concurrences do not provide necessary and sufficient conditions for entanglement detection

  • Authors:

  • Laura Cattaneo;Domenico D'alessandro

  • Affiliations:

  • Department of Mathematics, Imperial College London, London, United Kingdom and Department of Mathematics, Iowa State University, Ames IA;Department of Mathematics, Iowa State University, Ames IA

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2009

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Abstract

We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2 × 4 states of rank 2, we prove that generalized concurrences do not, in general, give a necessary and sufficient condition of separability. We identify a set of entangled states which are undetected by this method.