Abstract
A new family of positive, trace-preserving maps is introduced. It is defined using the mutually unbiased measurements, which generalize the notion of mutual unbiasedness of orthonormal bases. This family allows one to define entanglement witnesses whose indecomposability depends on the characteristics of the associated measurement operators. We provide examples of indecomposable witnesses and compare their entanglement detection properties with the realignment criterion.
Highlights
A new family of positive, trace-preserving maps is introduced
A quantum state represented by a density operator ρ on the Hilbert space H1 ⊗ H2 is separable if and only if it can be decomposed into ρ = k pkρk(1) ⊗ ρk(2), where ρk(1) and ρk(2) are density operators of two subsystems and pk is a probability distribution
There is one class related to the well-known realignment or computable cross-norm (CCNR) separability c riterion[7,8,9], and covariance matrix criterion[10,11,12]
Summary
A new family of positive, trace-preserving maps is introduced. It is defined using the mutually unbiased measurements, which generalize the notion of mutual unbiasedness of orthonormal bases. We further develop the construction of entanglement witnesses (in particular, indecomposable ones) in terms of MUMs, which generalize the notion of mutually unbiased bases (MUBs) to non-projective operators. Li et al used the MUMs to introduce new positive quantum maps and entanglement w itnesses[37] that generalize the construction from Ref.[16].
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