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Mathematical Physics

arXiv:2111.08216 (math-ph)
[Submitted on 16 Nov 2021]

Title:Second-order statistics of fermionic Gaussian states

Authors:Youyi Huang, Lu Wei
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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.
Comments: 23 pages, 3 figures
Subjects: Mathematical Physics (math-ph); Information Theory (cs.IT); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Cite as: arXiv:2111.08216 [math-ph]
  (or arXiv:2111.08216v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.2111.08216
Journal reference: J. Phys. A: Math. Theor. 55 105201, 2022
Related DOI: https://doi.org/10.1088/1751-8121/ac4e20

Submission history

From: Lu Wei [view email]
[v1] Tue, 16 Nov 2021 04:18:25 UTC (158 KB)
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