Second-order statistics of fermionic Gaussian states
arXiv:2111.08216 · doi:10.1088/1751-8121/ac4e20
Abstract
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.
arXiv comment23 pages, 3 figures
References in corpus (22)
- Average Entropy of a Subsystem
- Statistical properties of random density matrices
- Random Bures mixed states and the distribution of their purity
- Aspects of capacity of entanglement
- The Page Curve for Fermionic Gaussian States
- Random pure states: quantifying bipartite entanglement beyond the linear statistics
- Distribution of bipartite entanglement for random pure states
- A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
- Eigenstate capacity and Page curve in fermionic Gaussian states
- Average Entropy of a Subsystem from its Average Tsallis Entropy
- Minimal energy cost of entanglement extraction
- Bures-Hall Ensemble: Spectral Densities and Average Entropies
- Exact variance of von Neumann entanglement entropy over the Bures-Hall measure
- Capacity of Entanglement in Local Operators
- Skewness of von Neumann entanglement entropy
- Capacity of entanglement in random pure state
- On the exact variance of Tsallis entropy in a random pure state
- Purity distribution for generalized random Bures mixed states
- Proof of Sarkar-Kumar's Conjectures on Average Entanglement Entropies over the Bures-Hall Ensemble
- Multiplicative Convolution of Real Asymmetric and Real Antisymmetric Matrices
- Kurtosis of von Neumann entanglement entropy
- Moments of quantum purity and biorthogonal polynomial recurrence