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Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) mapswere previously introduced for the purpose of detection and quantification ofnonclassical correlation, employing the paradigm where nonvanishing quantumdiscord implies the existence of nonclassical correlation. It is known thatonly the matrix transposition is nontrivial among Hermiticity-preserving (HP)linear EnCE maps when we use the changes in the eigenvalues of a density matrixdue to a partial map for the purpose. In this paper, we prove that this is trueeven among not-necessarily HP (nnHP) linear EnCE maps. The proof utilizes aconventional theorem on linear preservers. This result imposes a stronglimitation on the linear maps and promotes the importance of nonlinear maps.

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