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Parallel repetition via fortification: analytic view and the quantum case

Bavarian, Mohammad and Vidick, Thomas and Yuen, Henry (2017) Parallel repetition via fortification: analytic view and the quantum case. In: 8th Innovations in Theoretical Computer Science Conference. Leibniz International Proceedings in Informatics. No.67. Dagstuhl Publishing , Art. No. 22. ISBN 9783959770293. https://resolver.caltech.edu/CaltechAUTHORS:20160321-071142064

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Abstract

In a recent work, Moshkovitz [FOCS'14] presented a transformation n two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.4230/LIPIcs.ITCS.2017.22DOIArticle
https://arxiv.org/abs/1603.05349arXivDiscussion Paper
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2017 Mohammad Bavarian, Thomas Vidick, and Henry Yuen; licensed under Creative Commons License CC-BY. Date of publication: 28.11.2017. The author was supported by NSF under CCF-0939370 and CCF-1420956. The author was supported by NSF CAREER Grant CCF-1553477, AFOSR YIP award number FA9550-16-1-0495, and the IQIM, an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028). The author was supported by Simons Foundation grant #360893, and National Science Foundation Grants 1122374 and 1218547.
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-0939370
NSFCCF-1420956
NSFCCF-1553477
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Simons Foundation360893
NSF Graduate Research FellowshipDGE-1122374
NSFCCF-1218547
Subject Keywords:Parallel repetition, quantum entanglement, non-local games
Series Name:Leibniz International Proceedings in Informatics
Issue or Number:67
Classification Code:1998 ACM Subject Classification: F.1.3 Complexity Measures and Classes
Record Number:CaltechAUTHORS:20160321-071142064
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160321-071142064
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65499
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Mar 2016 20:33
Last Modified:28 Jul 2020 22:40

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