Quantum discord is a measure of quantum correlation beyond entanglement. Computing quantum discord for simple quantum states is a basic problem. An analytical formula of quantum discord for two-qubit $X$ states is first claimed in [Ali, Rau, and Alber, Phys. Rev. A 81, 042105 (2010)], but later found to be not always correct. I observe numerically that the formula is valid with worst-case absolute error 0.0021. For symmetric two-qubit $X$ states, I give a counterexample to the analytical formula derived in [F. F. Fanchini et al., Phys. Rev. A 81, 052107 (2010)], but observe that the formula is valid with worst-case absolute error 0.0006. The formula has been used in many research papers. The results in all these works are approximately correct, even if they may not be exactly correct.

• Received 7 April 2013

DOI:https://doi.org/10.1103/PhysRevA.88.014302