Revisiting Quantum discord for two-qubit X states: Error bound to Analytical formula

TL;DR

This paper evaluates the accuracy of existing analytical formulas for quantum discord in two-qubit X states, establishing error bounds and highlighting potential worst-case deviations.

Contribution

It provides error bounds for two analytical formulas of quantum discord in X states, clarifying their precision and limitations.

Findings

Ali et al.'s formula has a worst-case error of 0.004565 for general X states.

Fanchini et al.'s formula has a worst-case error of 0.0009 for symmetric X states.

The results inform the reliability of these formulas in quantum information applications.

Abstract

In this article, we investigate the error bound of quantum discord, obtained by the analytic formula of Ali et al.[Phys. Rev. A 81(2010), 042105] in case of general X states and by the analytic formula of Fanchini et al.[Phys. Rev. A 81(2010), 052107] in case of symmetric X states. We show that results of Ali et. al. to general X states and Fanchini et al. to symmetric X states may have worst-case error of 0.004565 and 0.0009 respectively.