Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

Abstract

In this article, we investigate the error bound of quantum discord, obtained from the analytic formula of Ali et al. (Phys. Rev. A 81, 042105, 2010) for the case of general X states and from the analytic formula of Fanchini et al. (Phys. Rev. A 81, 052107, 2010) for the case of symmetric X states. For this purpose we consider 3-element POVM. We find that the results of Ali et al. and Fanchini et al. may have the worst-case errors of 0.004565 and 0.0009, respectively.