Tractable measure of nonclassical correlation using density matrix truncations

TL;DR

This paper introduces a polynomial-time computable measure of nonclassical correlation based on density matrix truncations, offering a practical alternative to traditional measures despite some limitations in detection range.

Contribution

It proposes a novel, efficient measure of nonclassical correlation using density matrix truncations, contrasting with existing methods that are often computationally intensive.

Findings

The measure is computable in polynomial time.

It has well-studied mathematical properties.

It provides a new physical interpretation of nonclassical correlation.

Abstract

In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of this paradigm, we propose a measure of nonclassical correlation by using truncations of a density matrix down to individual eigenspaces. It is computable within polynomial time in the dimension of the Hilbert space albeit imperfect in the detection range. This is in contrast to the measures conventionally used for the paradigm. The computational complexity and mathematical properties of the proposed measure are investigated in detail and the physical picture of its definition is discussed.