  A method for calculating the one-way quantum deficit is developed. It
involves a careful study of post-measured entropy shapes.
  We discovered that in some regions of X-state space the post-measured entropy
$\tilde S$ 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. Furthermore, cases are found
when the interior minimum of such a bimodal function
  $\tilde S(\theta)$ is less than that one at the endpoint $\theta=0$ or
$\pi/2$.
  This leads to the formation of a boundary between the phases of one-way
quantum deficit via
  {\em finite} jumps of optimal measured angle from the endpoint to the
interior minimum. Phase diagram is built up for a two-parameter family of X
states. The subregions with variable optimal measured angle are around 1$\%$ of
the total region, with their relative linear sizes achieving $17.5\%$, and the
fidelity between the states of those subregions can be reduced to $F=0.968$.
  In addition, a correction to the one-way deficit due to the interior minimum
can achieve
  $2.3\%$. Such conditions are favorable to detect the subregions with variable
optimal measured angle of one-way quantum deficit in an experiment.
