Calculation of the quantum discord requires to find the minimum of the quantum conditional entropy S(ρAB|{ΠBk}) over all measurements on the subsystem B. In this paper, we provide a simple relation for the conditional entropy as the difference of two Shannon entropies. The relation is suitable for calculation of the quantum discord in the sense that it can be used to obtain the quantum discord for some classes of two-qubit states such as Bell-diagonal states and a three-parameter subclass of X states, without the need for minimization. We also present an analytical procedure of optimization and obtain conditions under which the quantum conditional entropy of a general two-qubit state is stationary. The presented relation is also used to find a tight upper bound on the quantum discord.

Keywords