Mathematical framework for detection and quantification of nonclassical correlation

TL;DR

This paper introduces a new, computationally efficient framework for detecting and quantifying nonclassical correlations in bipartite systems using eigenvalue-preserving maps, inspired by entanglement theory.

Contribution

It proposes a novel class of eigenvalue-preserving maps (EnCE) for measuring nonclassical correlations, offering a less costly alternative to existing methods.

Findings

EnCE maps are effective in detecting nonclassical correlations.

The measures based on EnCE maps are shown to be subadditive.

The framework generalizes concepts from entanglement theory to broader nonclassical correlations.

Abstract

Existing measures of bipartite nonclassical correlation that is typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps. The class is in analogy to the class of positive-but-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 in a form of logarithmic fidelity.