Symmetric quantum discord for a two-qubit state

You-neng Guo, Ke Zeng, Guo-You Wang

Zhongxiao Wang, Bobo Wang

We discuss the symmetric quantum discord (SQD) for an arbitrary two-qubit state consisting of subsystems A and B and give the analysis formula of the symmetric quantum discord for the arbitrary two-qubit state. We also give the optimization process of the symmetric quantum discord for some states and obtain the symmetric quantum discord. We compare the quantum discord (QD) with the symmetric quantum discord, and find that the symmetric quantum discord is greater than the quantum discord. We also find that the symmetric quantum discord can be unequal to the quantum discord when the right quantum discord (measure on subsystem B) is equal to the left quantum discord (measure on subsystem A).

Jianming Zhou, Xiaoli Hu, Naihuan Jing

Yichen Huang

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.

Jing Nie, Xiu-Yi Yang, Chong Li

Min Namkung, Jinho Chang, Jaehee Shin +1 more

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.