Mathematical framework for detection and quantification of nonclassical correlation

Existing measures of bipartite nonclassical correlations that are typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in the computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completelyeigenvalue-preserving (EnCE) maps. The class is in analogy to the class of positivebut-not-completely-positive (PnCP) maps that have been commonly used in the entanglement theories. Linear and nonlinear EnCE maps are investigated. We also prove subadditivity of the measures derived from the maps. PACS numbers: 03.65.Ud, 03.67.Mn, 03.65.Ta Mathematical framework for detection and quantification of nonclassical correlations 2