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

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.Comment: 14 pages, 8 figure

Design of Optimal Topology of Satellite-Based Terrestrial Communication Networks

Topological design of terrestrial networks for communication via satellites is studied in the paper. Quantitative model of the network cost-analysis minimizing the total transmission and switching cost is described. Several algorithms solving combinatorial problem of the optimal topology design based on binary partitioning, a minimax parametric search and dynamic programming are developed by the author and demonstrated with a numeric example. Analysis of average complexity of the minimax parametric search algorithm is also provided.Comment: Journal of Telecommunications,Volume 1, Issue 1, pp25-35, February 201