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

Author： Jamiołkowski A.  

Publisher： Springer Publishing Company

ISSN： 1230-1612

Source： Open Systems and Information Dynamics, Vol.11, Iss.4, 2004-12, pp. : 385-390

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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.

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