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Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement.

ABSTRACT: Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric measure of entanglement. On the one hand, we first provide a semidefinite algorithm to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states. Based on this semidefinite algorithm, we test randomly generated single-qubit states, single-qutrit states, and a special kind of d-dimensional mixed states. Moreover, we also obtain an analytical solution of geometric measure of coherence for a special kind of mixed states. On the other hand, another algorithm is proposed to calculate the geometric measure of entanglement for arbitrary two-qubit and qubit-qutrit states, and some special kinds of higher dimensional mixed states. For other states, the algorithm can get a lower bound of the geometric measure of entanglement. Randomly generated two-qubit states, the isotropic states and the Werner states are tested. Furthermore, we compare our numerical results with some analytical results, which coincide with each other.

SUBMITTER: Zhang Z

PROVIDER: S-EPMC7374728 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement.

Zhang Zhou Z Dai Yue Y Dong Yu-Li YL Zhang Chengjie C

Scientific reports 20200721 1

Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric measure of entanglement. On the one hand, we first provide a semidefinite algorithm to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states. Based on this semidefinite algorithm, we test randomly generated single-q ...[more]

PMID: 32694576

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Project description:Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson's ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts-one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson's ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler-Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson's ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson's ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson's ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.

Project description:Objective:The geometric configuration of the intraventricular tunnel is related to the re-intervention of left ventricular outflow tract stenosis after double outlet right ventricle (DORV) correction. Hemodynamic simulation was performed in order to study the influence of the geometric configuration of the IVT on the pressure difference. Methods:CT images of DORV were processed to reconstruct 3D models of left and right ventricular flow chambers and aortic valve orifice, and then the size and relative position of the aortic valve orifice and ventricular septal defect were determined. Twenty five groups of the idealized models were established according to orthogonal test design and computational fluid dynamics method was applied to simulate hemodynamics. Three factors of geometric configuration were considered for the study of their influences on the pressure difference. The first factor is the distance between the ventricular septal defect and the plane of the aortic valve (DSA), the second factor is the ejection angle of blood from left ventricle flowing into the IVT (ALT), and the third factor is the turning radius of the IVT (RTT). SPSS software was employed to perform the orthogonal analysis. Additionally, twelve models with different turning radii were established for hemodynamic analysis, with the turning radii increasing from 0 mm with an interval of 1 mm, so as to study the influence of turning radius on pressure difference of IVT. Results:The analysis of variance showed that only the change of RTT had a significant effect on the pressure difference (P = 0 < 0.05), while the change of DSA and ALT had no significant effect on the pressure difference (P = 0.459 > 0.05, P = 0.263 > 0.05). The pressure difference decreases with the increase of RTT. When RTT reaches 6 mm, the pressure difference gradually remains unchanged with the increase of RTT, and the rate of change is less than 5%. Conclusion:RTT in the IVT is the main factor affecting the pressure difference. A small RTT will lead to a large pressure difference in the IVT. When RTT increases to 6 mm, the pressure difference in the IVT remains nearly unchanged. When performing the right ventricular double outlet correction; the turning radius of the IVT should be about 6 mm to ensure relatively small pressure difference.

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Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement.

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Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement.

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