{"id":{"repo_id":"ttu","oai_identifier":"oai:ttu-ir.tdl.org:2346/99181"},"canonical_url":"https://search.dev.ndltd.org/etd/ttu/oai:ttu-ir.tdl.org:2346/99181","repository":{"repo_id":"ttu","name":"Texas Technology University","base_url":"https://ttu-ir.tdl.org/server/oai/request"},"display":{"title":"Higher-order moments of entanglement estimators over generic state ensembles","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Huang, Youyi"],"institution":"Texas Tech University","degree_name":"Doctor of Philosophy","degree_level":null,"degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":["Wei, Lu"],"committee_members":["Zhuang, Yu","Liu, Ying","Ji, Tianxi"],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-24T05:04:51Z","subjects":["Quantum information","von Neumann entropy","Random Matrix Theory","Orthogonal Polynomials","Special Functions"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2346/99181","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Wei, Lu"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Zhuang, Yu","Liu, Ying","Ji, Tianxi"]},{"key":"dc:creator","label":"Author","values":["Huang, Youyi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-07-25T14:47:10Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-07-25T14:47:10Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-05"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Texas Tech University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Quantum information","von Neumann entropy","Random Matrix Theory","Orthogonal Polynomials","Special Functions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2346/99181"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Higher-order moments of entanglement estimators over generic state ensembles"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Wei, Lu"],"dc:contributor.committeemember":["Zhuang, Yu","Liu, Ying","Ji, Tianxi"],"dc:creator":["Huang, Youyi"],"dc:date.accessioned":["2024-07-25T14:47:10Z"],"dc:date.available":["2024-07-25T14:47:10Z"],"dc:date.issued":["2024-05"],"dc:description.abstract":["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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2346/99181"],"dc:language.iso":["eng"],"dc:subject":["Quantum information","von Neumann entropy","Random Matrix Theory","Orthogonal Polynomials","Special Functions"],"dc:title":["Higher-order moments of entanglement estimators over generic state ensembles"],"dc:type":["Thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Texas Tech University"]},"updated_at":"2026-07-24T05:04:51Z"}