The structure of optimal and nearly-optimal quantum strategies for non-local XOR games
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2015
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| Online Access: | http://hdl.handle.net/1721.1/99065 |
| _version_ | 1826207722282942464 |
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| author | Ostrev, Dimiter |
| author2 | Peter Shor. |
| author_facet | Peter Shor. Ostrev, Dimiter |
| author_sort | Ostrev, Dimiter |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. |
| first_indexed | 2024-09-23T13:53:56Z |
| format | Thesis |
| id | mit-1721.1/99065 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:53:56Z |
| publishDate | 2015 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/990652019-04-10T08:47:44Z The structure of optimal and nearly-optimal quantum strategies for non-local XOR games Ostrev, Dimiter Peter Shor. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. Cataloged from PDF version of thesis. Includes bibliographical references (pages 99-101). We study optimal and nearly-optimal quantum strategies for non-local XOR games. First, we prove the following general result: for every non-local XOR game, there exists a set of relations with the properties: (1) a quantum strategy is optimal for the game if and only if it satisfies the relations, and (2) a quantum strategy is nearly optimal for the game if and only if it approximately satisfies the relations. Next, we focus attention on a specific infinite family of XOR games: the CHSH(n) games. This family generalizes the well-known CHSH game. We describe the general form of CHSH(n) optimal strategies. Then, we adapt the concept of intertwining operator from representation theory and use that to characterize nearly-optimal CHSH(n) strategies by Dimiter Ostrev. Ph. D. 2015-09-29T19:01:12Z 2015-09-29T19:01:12Z 2015 2015 Thesis http://hdl.handle.net/1721.1/99065 921854255 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 101 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Ostrev, Dimiter The structure of optimal and nearly-optimal quantum strategies for non-local XOR games |
| title | The structure of optimal and nearly-optimal quantum strategies for non-local XOR games |
| title_full | The structure of optimal and nearly-optimal quantum strategies for non-local XOR games |
| title_fullStr | The structure of optimal and nearly-optimal quantum strategies for non-local XOR games |
| title_full_unstemmed | The structure of optimal and nearly-optimal quantum strategies for non-local XOR games |
| title_short | The structure of optimal and nearly-optimal quantum strategies for non-local XOR games |
| title_sort | structure of optimal and nearly optimal quantum strategies for non local xor games |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/99065 |
| work_keys_str_mv | AT ostrevdimiter thestructureofoptimalandnearlyoptimalquantumstrategiesfornonlocalxorgames AT ostrevdimiter structureofoptimalandnearlyoptimalquantumstrategiesfornonlocalxorgames |