We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states as measured by von Neumann entropy and entanglement capacity. The focus is on the variance of von Neumann entropy and the mean entanglement capacity that belong to the so-defined second-order statistics. The main results are the exact yet explicit formulas of the two considered second-order statistics for fixed subsystem dimension differences. We also conjecture the exact variance of von Neumann entropy valid for arbitrary subsystem dimensions. Based on the obtained results, we analytically study the numerically observed phenomena of Gaussianity of von Neumann entropy and linear growth of average capacity.
翻译:我们研究以冯纽曼的酶和缠绕能力测量的高斯州在量子双边系统中的纠缠的统计行为,重点是冯纽曼的酶的变异和属于如此定义的第二阶统计的中度缠绕能力。主要结果就是两个被视为固定子系统维度差异第二阶层统计的精确而明确的公式。我们还预测了冯纽曼的酶的精确变异,这些变异适用于任意的子系统维度。根据获得的结果,我们分析了冯纽曼的酶酶的数值观测现象和平均容量的直线增长。