The geometric approach to quantum correlations: Computability versus reliability

TL;DR

This paper introduces a modified geometric measure of quantum discord based on a Hilbert-Schmidt norm, balancing computability and reliability in quantifying quantum correlations.

Contribution

It proposes a new metric for quantum discord that avoids purity dependence and assesses the trade-offs between reliability and computability.

Findings

New metric reduces purity dependence

Agreement with existing discord measures in examples

Highlights reliability versus computability issues

Abstract

We propose a modified metric based on the Hilbert-Schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord. Such a measure is found not to suffer from the pathological dependence on state purity. Although the employed metric is still noncontractive under quantum operations, we show that the resulting indicator of quantum correlations is in agreement with other bona fide discord measures in a number of physical examples. We present a critical assessment of the requirements of reliability versus computability when approaching the task of quantifying, or measuring, general quantum correlations in a bipartite state.