Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states

M. A. Yurischev

paper

Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states

arXiv:1706.02852

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 $θ \in [0, π /2]$ 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.

arXiv comment14 pages, 8 figures

Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states

Abstract

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