Entropy Fluctuation Formulas of Fermionic Gaussian States

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 wor...

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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 24; no. 12; pp. 4283 - 4342
Main Authors Huang, Youyi, Wei, Lu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2023
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Entropy
Hypergeometric functions
Mathematical and Computational Physics
Mathematical Methods in Physics
Original Paper
Physics
Physics and Astronomy
Quantum entanglement
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
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Summary: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. As a by-product, the proposed framework leads to various new transformation formulas of hypergeometric functions.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-023-01342-w