Bimodal behavior of measurement-dependent one-way quantum deficit for two-qubit X states

It is shown that in some regions of X-state space the measurement-dependent one-way quantum deficit \Delta as a function of measurement angle \theta\in[0,\pi/2] exhibits a bimodal behavior inside the open interval (0,\pi/2), i.e., it has two interior extrema: one minimum and one maximum. Moreover, cases are found when the interior minimum of such a bimodal function \Delta(\theta) is less than that one at the endpoint with \theta=0 or \theta=\pi/2. This refutes the result of Ye et al. [Int. J. Theor. Phys. {\bf 55}, 2237 (2016)] which was intended for obtaining the one-way quantum deficit of general two-qubit X states.