Higher-order moments of entanglement estimators over generic state ensembles

The degree of entanglement of quantum bipartite systems can be estimated quantitatively by the entanglement indicators including the von Neumann entropy and entanglement capacity. This work focuses on the statistical behavior of the entanglement indicators over two generic state ensembles -- the Hilbert-Schmidt ensemble and the fermionic Gaussian ensemble. For the Hilbert-Schmidt ensemble, expressions of the first three exact cumulants of von Neumann entropy are known in the literature. In the present work, we derive the exact formula of the corresponding fourth cumulant that controls the tail behavior of the distribution. For the fermionic Gaussian ensemble, the formulas of average von Neumann entropy with and without particle number constraints have been recently obtained, whereas the main results of this work include the exact yet explicit formulas of variances for both cases. Furthermore, the exact mean value formulas of entanglement capacity are also derived.

Name thesis:degree_name

Doctor of Philosophy

Discipline thesis:degree_discipline

Computer Science

Grantor

Texas Tech University

Year dc:date.issued

2024

Author dc:creator

• Huang, Youyi

Chair dc:contributor.committeechair

• Wei, Lu

Committee members dc:contributor.committeemember

• Zhuang, Yu
• Liu, Ying
• Ji, Tianxi

• Quantum information
• von Neumann entropy
• Random Matrix Theory
• Orthogonal Polynomials
• Special Functions

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/2346/99181

OAI identifier oai:identifier

oai:ttu-ir.tdl.org:2346/99181