Correlation between concurrence and mutual information

TL;DR

This paper explores the relationship between quantum entanglement and classical information in a two-qubit system, revealing a positive correlation that suggests classical measurements can estimate quantum entanglement.

Contribution

It provides a statistical analysis of the correlation between concurrence and mutual information in random pure states, highlighting the potential to assess quantum entanglement through classical information.

Findings

Zero mutual information is most probable in the ensemble.

Positive correlation exists between concurrence and mutual information.

Classical information can be used to estimate quantum entanglement.

Abstract

We investigate a two-qubit system to understand the relationship between concurrence and mutual information, where the former determines the amount of quantum entanglement, whereas the latter is its classical residue after performing local projective measurement. For a given ensemble of random pure states, in which the values of concurrence are uniformly distributed, we calculate the joint probability of concurrence and mutual information. Although zero mutual information is the most probable in the uniform ensemble, we find positive correlation between the classical information and concurrence. This result suggests that destructive measurement of classical information can be used to assess the amount of quantum information.