Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation

Details Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation

2010-12-28

arxiv.org/abs/1012.5718v2

Physics

Quantum Physics

13 pages, no figure, v1: 6 pages, no figure, v2: minor revision, style changed, proofs in Section 4 changed

Scientific paper

Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps were previously introduced for the purpose of detection and quantification of nonclassical correlation, employing the paradigm where nonvanishing quantum discord implies the existence of nonclassical correlation. It is known that only the matrix transposition is nontrivial among Hermiticity-preserving (HP) linear EnCE maps when we use the changes in the eigenvalues of a density matrix due to a partial map for the purpose. In this paper, we prove that this is true even among not-necessarily HP (nnHP) linear EnCE maps. The proof utilizes a conventional theorem on linear preservers. This result imposes a strong limitation to the linear maps and promotes the importance of nonlinear maps.

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