Quantum Discord for $d\otimes2$ Systems

TL;DR

This paper derives an analytical solution for classical correlation in $d\otimes 2$ quantum systems using linear entropy and establishes a tight upper bound for quantum discord in terms of von Neumann entropy, validated by numerical analysis.

Contribution

It provides the first analytical solution for classical correlation in $d\otimes 2$ systems and a tight upper bound for quantum discord applicable to arbitrary systems.

Findings

Analytical solution for classical correlation in $d\otimes 2$ systems.

Tight upper bound for quantum discord in $d\otimes 2$ systems.

Numerical validation with high accuracy for random two-qubit states.

Abstract

We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary $d\otimes 2$ system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary $d\otimes 2$ systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for $10^6$ two-qubit random density matrices, we obtain an average deviation of order $10^{-4}$. Furthermore, our results give a way to calculate the quantum discord for arbitrary $n$-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel.