Projectivities of Informationally Complete Measurements

The physical problem behind informationally complete (IC) measurements is determining an unknown state statistically by measurement outcomes, known as state tomography. It is of central importance in quantum information processing such as channel estimating, device testing, quantum key distribution, etc. However, constructing such measurements with good properties is a long-standing problem. In this work, projective realizations of IC measurements are investigated. Conditions of informational completeness are presented with proofs first. Then the projective realizations of IC measurements, including proposing the first general construction of minimal projective IC measurements (MPICM) in no prime power dimensional systems, as well as determining an unknown state in $C^n$ via a single projective measurement with some kinds of optimalities in a larger system, are investigated. Finally, The results can be extended to local state tomography. Some discussions on employing several kinds of optimalities are also provided.     

An approach utilizing the Response Surface Methodology (RSM) to optimize Adsorption-Desorption of Natural Saudi Arabian Diatomite- with the Box- Behnken Design Technique

Saudi Arabian’s natural diatomite samples were subjected to physical adsorption–desorption characterizations using Brunauer-Emmet-Teller (BET) and the Barrett-Joyner-Halenda (BJH), performed under heating of 140 °C for different periods of hours: 6, 12, 18, and 24 h, to create a central optimization design with surface areas and total pore distributions. Seventeen experimental runs resulted in the primary composite factor design. The surface response describes 100 % variability with a determination coefficient of 1, signifying the quadratic model with an expected correlation coefficient (R²) is satisfied with a standard deviation of 0.2322, demonstrating the high predictability of the model. Moreover, the RSM results have been validated using the t-test with the observed R² value and adjusted R². The model selected with higher F and p values showed<0.0001, which subsequently described the significance of the developed model. The independent components were explained with the help of 3D surface and contour plots that compare the heating time, elapsed time, pressure, and relative pressure against the dependent variable. The plots revealed that the adsorbed quantities well depended on heating time, elapsed time, pressure, relative pressure for isotherm, BET surface area, Langmuir surface area, and t-plot Micropore area.