Concentration Bounds from Parallel Repetition Theorems
| dc.contributor.author | Hornby, Taylor | |
| dc.date.accessioned | 2018-08-22T16:57:55Z | |
| dc.date.available | 2018-08-22T16:57:55Z | |
| dc.date.issued | 2018-08-22 | |
| dc.date.submitted | 2018-08-17 | |
| dc.description.abstract | This thesis contributes to the study of parallel repetition theorems and concentration bounds for nonlocal games and quantum interactive proofs. We make the following contributions: - A lemma that is useful for converting parallel repetition theorems (bounds on the probability of winning all instances of a nonlocal game which is being repeated in parallel) into concentration bounds (bounds on winning a certain fraction of the instances). - Exponentially-decaying concentration bounds for two-player games on the uniform distribution and k-player free games, against quantum strategies. - A proof that given a quantum interactive proof system with parameters α (the probability with which the verifier can be convinced to accept when they should accept) and β (the soundness error), as long as α > β, both the soundness error and completeness error can be reduced exponentially by repeating the protocol in parallel and requiring an (α + β)/2 fraction of the repetitions to be won. Our result requires a log-factor more repetitions than are necessary in the classical case. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/13638 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | quantum information | en |
| dc.subject | parallel repetition | en |
| dc.subject | nonlocal games | en |
| dc.subject | interactive proofs | en |
| dc.subject | concentration bounds | en |
| dc.title | Concentration Bounds from Parallel Repetition Theorems | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | David R. Cheriton School of Computer Science | en |
| uws-etd.degree.discipline | Computer Science (Quantum Information) | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws.contributor.advisor | Watrous, John | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |