Rigidity of near-optimal superdense coding protocols

dc.contributor.authorZhou, Xingyu
dc.date.accessioned2023-09-19T13:53:16Z
dc.date.available2023-09-19T13:53:16Z
dc.date.issued2023-09-19
dc.date.submitted2023-08-29
dc.description.abstractRigidity in quantum information theory refers to the stringent constraints underlying optimal or near-optimal performance in certain quantum tasks. This property plays a crucial role in verifying untrusted quantum devices and holds significance for secure quantum protocols. Previous work by Nayak and Yuen demonstrated that all optimal superdense coding protocols are locally equivalent to the canonical Bennett-Wiesner protocol. For higher-dimensional superdense coding protocols, Nayak and Yuen showed they may exist only in a relaxed form, and Farkas, Kaniewski and Nayak showed there are infinitely many dimensions $d\geq 4$ such that the rigidity does not exist even in the relaxed form. Our work is dedicated to establishing the rigidity properties of near-optimal superdense coding protocols. Specifically, we explore scenarios where Alice can employ finite but arbitrary ancilla qubits for encoding, Bob can perform positive operator-valued measure (POVM) for decoding and can answer with error. In such contexts, we prove that any near-optimal superdense coding must be locally equivalent to a superdense coding protocol close to the canonical Bennett-Wiesner protocol. In the search for extending the result to higher dimensional superdense coding protocols, we find a method to orthogonalize any two unitary matrices in the same space. However, the question of whether it is feasible to orthogonalize more than two $d\times d$ unitary matrices when $d>2$ remains an intriguing yet unresolved matter.en
dc.identifier.urihttp://hdl.handle.net/10012/19886
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectsuperdense codingen
dc.subjectself-testingen
dc.subjectrigidityen
dc.subjectquantum informationen
dc.titleRigidity of near-optimal superdense coding protocolsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimization (Quantum Information)en
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorNayak, Ashwin
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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