The More the Merrier

: Resource Preservation and Enhancement in Quantum Resource Theories

Abstract

Resource theories provide a rigorous mathematical framework for quantifying and studying different quantum phenomena; they achieve this by studying the limitations placed on a system by a set of physical constraints. Through this operational approach, they have successfully been used to understand a diverse range of properties, including those of quantum states, measurements and dynamics.

Within this framework, questions about resource preservation and resource enhancement are of both practical and fundamental interest. The first part of this thesis investigates the notion of resource preservation and enhancement within the resource theories of informational non-equilibrium, unspeakable coherence, and athermality. First, the framework of resource preservability theories is applied to the resource theory of informational non-equilibrium, yielding a characterisation of the ability of the allowed operations to preserve informational non-equilibrium (the resource). To achieve this, resource preservation itself is treated as a dynamical resource, leading to the definition of a dynamical resource theory over the set of allowed operations. Secondly, the framework of resource concentration is introduced to study the minimal feasible scenario of local resource enhancement under resource non-generating operations. This framework is applied to both the resource theory of informational non-equilibrium and the resource theory of unspeakable coherence, with insights gained from this minimal case then applied to gain an understanding of resource enhancement in more general cases. Finally, local resource enhancement via resource-generating operations is investigated within the resource theory of athermality, specifically in the context of cooling. The effect of the energetic structure of a machine composed of $n$ thermal qubits on its ability to cool an additional thermal qubit via energy non-conserving unitary dynamics is analysed. A set of inequalities characterising the optimal achievable cooling, the protocols that attain it, and their associated complexity is found.

In the second part of this thesis, the Choi-state, an indispensable tool in the study and analysis of quantum channels, is investigated. Specifically, the Choi-rank is shown to provide a universal bound on how successfully two agents can perform in an entanglement-assisted exclusion task. To achieve this, our understanding of the task of conclusive $k$-state exclusion in general is developed.

Date of Award	17 Mar 2026
Original language	English
Awarding Institution	University of Bristol
Supervisor	Paul Skrzypczyk (Supervisor) & Chung-Yun Hsieh (Supervisor)