Optimizing and generalizing quantum fidelities

Afham

Optimizing and generalizing quantum fidelities

Afham

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Publication Type:: Thesis
Issue Date:: 2025

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Field	Value	Language
dc.contributor.author	Afham
dc.date.accessioned	2025-10-27T22:26:43Z
dc.date.available	2025-10-27T22:26:43Z
dc.date.issued	2025
dc.identifier.uri	http://hdl.handle.net/10453/190570
dc.description	University of Technology Sydney. Faculty of Engineering and Information Technology.	en_US.UTF-8
dc.description.abstract	This thesis presents new theoretical and computational advances in quantum fidelities—core metrics for comparing quantum states. It addresses three main problems. First, it introduces a semidefinite program and scalable fixed-point algorithms to find states that maximize average fidelity over quantum ensembles, yielding new bounds and practical tools for tasks such as Bayesian quantum tomography. Second, it proposes a generalized family of fidelities based on the Riemannian geometry of the Bures–Wasserstein manifold, unifying and offering novel geometric interpretations of Uhlmann, Holevo, and Matsumoto fidelities. Third, it investigates fidelity-based projections of positive matrices onto convex sets defined by quantum channels, deriving closed-form solutions in key cases such as the partial trace. These results enable applications in quantum process tomography and random state generation while providing new geometric insights into the pretty good measurement and Petz recovery map. Overall, this thesis contributes to the advancement of practical quantum information processing by addressing core optimization problems involving fidelity—problems that are central to many theoretical and applied areas of quantum information science.	en_US.UTF-8
dc.format	Thesis (PhD)
dc.language.iso	en_US	en_US.UTF-8
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/190570/1/thesis.pdf
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.rights	© 2025 Afham
dc.rights	au.edu.uts.lib/cph
dc.title	Optimizing and generalizing quantum fidelities	en_US.UTF-8
dc.type	Thesis
utslib.copyright.status	open_access	*

Abstract:

This thesis presents new theoretical and computational advances in quantum fidelities—core metrics for comparing quantum states. It addresses three main problems. First, it introduces a semidefinite program and scalable fixed-point algorithms to find states that maximize average fidelity over quantum ensembles, yielding new bounds and practical tools for tasks such as Bayesian quantum tomography. Second, it proposes a generalized family of fidelities based on the Riemannian geometry of the Bures–Wasserstein manifold, unifying and offering novel geometric interpretations of Uhlmann, Holevo, and Matsumoto fidelities. Third, it investigates fidelity-based projections of positive matrices onto convex sets defined by quantum channels, deriving closed-form solutions in key cases such as the partial trace. These results enable applications in quantum process tomography and random state generation while providing new geometric insights into the pretty good measurement and Petz recovery map. Overall, this thesis contributes to the advancement of practical quantum information processing by addressing core optimization problems involving fidelity—problems that are central to many theoretical and applied areas of quantum information science.

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http://hdl.handle.net/10453/190570