Abstract
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 S as a function of measurement angle θ∈[0,π/2] exhibits a bimodal behavior inside the open interval (0,π/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 S(θ) is less than that one at the endpoint θ=0 or π/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.