Some Remarks on the Role of Minimal Length of Positive Maps in Constructing Entanglement Witnesses

  • Authors:

  • A. Jamiołkowski

  • Affiliations:

  • Institute of Physics, Nicolaus Copernicus University, Toruń, Poland 87-100

  • Venue:
  • Open Systems & Information Dynamics
  • Year:
  • 2004

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Abstract

The main objective of this paper is to discuss correspondence between the concept of entanglement witnesses (self-adjoint operators on a composite Hilbert space $${\cal H} = {\cal H}_1 \otimes {\cal H}_2$$ that are, in general, not positive, but are positive on separable states) and positive maps $$\Phi : L({\cal H}_1) \to L({\cal H}_2)$$ which are not completely positive. The notion of minimal length of linear positive map is introduced and the role of this quantity in the constructing of entanglement witnesses is explained.