Noisy Interactive Quantum Communication

dc.contributor.authorShayeghi, Ala
dc.date.accessioned2020-08-25T20:28:02Z
dc.date.available2020-08-25T20:28:02Z
dc.date.issued2020-08-25
dc.date.submitted2020-08-18
dc.description.abstractWe consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with n messages, designed for noiseless qudit channels (where d is arbitrary), our main result is a simulation method that fails with probability less than 2⁻ᶿ⁽ⁿᵋ⁾ and uses a qudit channel n(1 + Θ(√ε)) times, of which ε fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the √ε term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Surprisingly, this outperforms the best known overhead of 1 + O(√(ε log log 1/ε)) in the corresponding classical model, which is also conjectured to be optimal [Haeupler, FOCS’14]. Our work also improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS’14] for small ε.en
dc.identifier.urihttp://hdl.handle.net/10012/16161
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectquantum communication complexityen
dc.subjectcoding theoryen
dc.subjectinteractive communicationen
dc.subjectquantum channel capacityen
dc.titleNoisy Interactive Quantum Communicationen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimization (Quantum Information)en
uws-etd.degree.grantorUniversity of Waterlooen
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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