Convex geometry in the characterisation of quantum resources

Regula, Bartosz (2018) Convex geometry in the characterisation of quantum resources. PhD thesis, University of Nottingham.

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Various physical phenomena have found use as resources in quantum information processing tasks, and the study of their properties is necessary to provide optimal methods to harness their power. The thesis presents a series of results aiming to characterise the quantitative and operational aspects of general quantum resources, and in particular to establish methods applicable to a variety of resources and emphasise the similarities in their characterisation. Our approach relies on the underlying convex structure of quantum resource theories, employing techniques from convex analysis and optimisation to gain a better understanding of both the fundamental properties of quantum resources as well as our ability to manipulate them efficiently in information processing protocols such as resource distillation.

The first part of the thesis introduces a unified framework for resource quantification, establishing general properties of arbitrary convex quantum resource theories and providing insight into the common structure of many physically relevant resources. The second part of the thesis deals with the convex optimisation problems involved in the operational characterisation of two representative quantum resources, quantum entanglement and quantum coherence, where we in particular establish a detailed description of their distillation under several classes of operations, and introduce methods for the interconversion between the two resources. In the final part, we employ geometric methods to characterise the quantification of entanglement measures based on polynomial invariants and apply the results to investigate the monogamy properties of multipartite entanglement.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Adesso, Gerardo
Guta, M.
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 53316
Depositing User: Regula, Bartosz
Date Deposited: 29 Nov 2018 13:35
Last Modified: 08 Feb 2019 09:17

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