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

摘要

The main objective of this paper is to discuss correspondence between the concept of entanglement witnesses (self-adjoint operators on a composite Hilbert space H = H_1 directX H_2 that are, in general, not positive, but are positive on separable states) and positive maps Φ : L(H_1) → L(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.