论文标题
费米子高斯州的熵波动公式
Entropy fluctuation formulas of fermionic Gaussian states
论文作者
论文摘要
我们研究了通过von Neumann熵测量的双基因高斯状态上两部分系统中量子纠缠的统计行为。最近已经获得了有或没有粒子数量约束的平均von Neumann熵的公式，而这项工作的主要结果是两种情况的确切但明确的方差公式。对于后一种无颗粒数的限制的情况，结果解决了相应方差的最新猜想。与其他通用状态模型相比，计算方差的现有方法不同，证明这项工作结果的关键要素取决于新的简化框架。该框架由一组新工具组成，以简化我们称为虚拟求和和重新启动技术的有限总和。作为副产品，所提出的框架导致了多种超几何函数的新变换公式。
We study the statistical behaviour of quantum entanglement in bipartite systems over fermionic Gaussian states as measured by von Neumann entropy. The formulas of average von Neumann entropy with and without particle number constrains have been recently obtained, whereas the main results of this work are the exact yet explicit formulas of variances for both cases. For the latter case of no particle number constrain, the results resolve a recent conjecture on the corresponding variance. Different than existing methods in computing variances over other generic state models, the key ingredient in proving the results of this work relies on a new simplification framework. The framework consists of a set of new tools in simplifying finite summations of what we refer to as dummy summation and re-summation techniques. As a byproduct, the proposed framework leads to various new transformation formulas of hypergeometric functions.
