Manipulation of dynamical resources in quantum information theory

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Quantum channels can be regarded as the most fundamental objects in quantum mechanics. With the help of quantum resource theories, it was recently recognized that dynamical quantum systems (described by quantum channels) may exhibit phenomena such as entanglement and coherence, and can be utilized as resources in various operational tasks. In this dissertation, I characterize and quantify the coherence and magic of dynamical quantum systems, formulate interconversion conditions among pairs of channels, and quantify the performance of fixed programmable processors. Quantum resource theories are governed by constraints arising from physical or practical settings. Considering the absence of coherence and efficient classical simulability (two different notions of classicality) as practical constraints towards achieving quantum advantage, I develop the resource theories of dynamical coherence and dynamical magic, respectively. In developing the resource theory of coherence, the underlying principle I follow is that the free dynamical objects are those that can neither store nor manipulate coherence. This led me to identify classical channels as free elements in this theory. The development of the resource theory of multi-qubit magic channels is motivated by the need to estimate the classical simulation cost of multi-qubit quantum circuits. The set of completely stabilizer preserving operations is the largest known set of operations in the multi-qubit scenario that can be efficiently simulated classically, and as such, they are the perfect candidates for the free channels of this resource theory. In both these resource theories, I quantify the resources using various resource measures, and solve several single-shot resource interconversion problems including different types of resource cost and distillation. I also formulate a classical simulation algorithm to estimate the expectation value of an observable and show that its runtime depends on a dynamical magic monotone. Besides developing the above resource theories, I generalize Lorenz majorization to the channel domain and use it to find the necessary and sufficient conditions for interconversion among pairs of classical channels. Furthermore, I quantify the performance of a fixed programmable quantum processor and find a trade-off relation between the success probability and the average fidelity error in simulating a target unitary using the processor.
quantum, quantum information, resource theory
Saxena, G. (2023). Manipulation of dynamical resources in quantum information theory (Unpublished doctoral thesis). University of Calgary, Calgary, AB.