We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic formulas of average capacity of two different cases - with and without particle number constraints. For the later case, the obtained formulas generalize some partial results of average capacity in the literature. The key ingredient in deriving the results is a set of new tools for simplifying finite summations developed very recently in the study of entanglement entropy of fermionic Gaussian states.

翻译：我们研究了纠缠容量作为纠缠熵的替代方案，用于估计费米子高斯态上量子二分系统的纠缠程度。特别地，我们推导了两种不同情况（有粒子数约束和无粒子数约束）下平均容量的精确公式和渐近公式。对于无约束情况，所得公式推广了文献中关于平均容量的一些部分结果。推导这些结果的关键在于一组近期在研究费米子高斯态纠缠熵时发展出的用于简化有限求和的工具。