Quantum discord for general two--qubit states: Analytical progress

TL;DR

This paper introduces a reliable algorithm to evaluate quantum discord for all two-qubit states, extending previous methods for specific subclasses, and compares it with geometric discord to identify extremal states.

Contribution

The authors develop a comprehensive algorithm for calculating quantum discord in general two-qubit states, overcoming previous limitations and enabling detailed numerical analysis.

Findings

Quantum discord cannot be expressed in closed form for all two-qubit states.

The algorithm allows accurate numerical evaluation of quantum discord.

The maximum geometric discord is the square root of the quantum discord for two-qubit states.

Abstract

We present a reliable algorithm to evaluate quantum discord for general two--qubit states, amending and extending an approach recently put forward for the subclass of X--states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of non-classical correlations, namely the geometric discord. We identify the extremally non-classically correlated two--qubit states according to the (normalized) geometric discord, at fixed value of the conventional quantum discord. The latter cannot exceed the square root of the former for systems of two qubits.