Manipulation of dynamical resources in quantum information theory

dc.contributor.advisorGour, Gilad
dc.contributor.authorSaxena, Gaurav
dc.contributor.committeememberMuller, Markus
dc.contributor.committeememberCockett, Robin
dc.contributor.committeememberFeder, David
dc.contributor.committeememberSanders, Barry
dc.date2023-06
dc.date.accessioned2023-03-16T19:48:27Z
dc.date.available2023-03-16T19:48:27Z
dc.date.issued2023-03-14
dc.description.abstractQuantum 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.en_US
dc.identifier.citationSaxena, G. (2023). Manipulation of dynamical resources in quantum information theory (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.urihttp://hdl.handle.net/1880/115926
dc.identifier.urihttps://dx.doi.org/10.11575/PRISM/40790
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectquantumen_US
dc.subjectquantum informationen_US
dc.subjectresource theoryen_US
dc.subject.classificationPhysicsen_US
dc.subject.classificationPhysics--Theoryen_US
dc.titleManipulation of dynamical resources in quantum information theoryen_US
dc.typedoctoral thesisen_US
thesis.degree.disciplinePhysics & Astronomyen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
ucalgary.item.requestcopytrueen_US
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
ucalgary_2023_saxena_gaurav.pdf
Size:
3.07 MB
Format:
Adobe Portable Document Format
Description:
License bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
license.txt
Size:
2.62 KB
Format:
Item-specific license agreed upon to submission
Description: