Computable Cross-norm Criterion for Separability

Abstract

We describe a computable analytical criterion for separability of bipartite mixed states in arbitrary dimension. The criterion stipulates that a certain norm on the state space (the computable cross-norm) is bounded by 1 for separable states. The criterion is shown to be independent of the well-known positive partial transpose (PPT) criterion. In other words, the criterion detects some bound entangled states but fails for some free entangled states.

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Rudolph, O. Computable Cross-norm Criterion for Separability. Letters in Mathematical Physics 70, 57–64 (2004). https://doi.org/10.1007/s11005-004-0767-7

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  • entanglement
  • separability criteria
  • projective tensor norm
  • cross-norms