Entropy Fluctuation Formulas of Fermionic Gaussian States

Zhengqian Cheng, Chris A. Marianetti

Youyi Huang, Lu Wei

Abstract 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.

Yangyang Wang, Xiaofei Qi, Jinchuan Hou +1 more

In the present paper, quantum coherence of fermionic Gaussian states is investigated from the point of quantum resource theory. Some characterizations of m-mode (m≥1) incoherent fermionic Gaussian states and incoherent fermionic Gaussian channels are obtained, two quantification measures of fermionic Gaussian quantum coherence based on respectively the relative entropy and the Hellinger distance are proposed, and some formulas to calculate the value of these measures are established. It is shown that the m-mode fermionic Gaussian coherence is a quantum resource.

Jinhyeok Ryu, Jaeyoon Cho

Youyi Huang, Lu Wei

We study the statistical behavior 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 constraints 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 constraint, the results resolve a recent conjecture on the corresponding variance. Different than the existing methods in computing variances over other generic state models, 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.

Atharva Naik, Bijay Kumar Agarwalla, Manas Kulkarni