NDLI: Generalized Tsirelson Inequalities, Commuting-Operator Provers, and Multi-prover Interactive Proof Systems

Content Provider	IEEE Xplore Digital Library
Author	Ito, T. Kobayashi, H. Preda, D. Xiaoming Sun Yao, A.C.-C.
Copyright Year	2008
Description	Author affiliation: Sch. of Comput. Sci., McGill Univ., Montreal, QC (Ito, T.)
Abstract	A central question in quantum information theory and computational complexity is how powerful nonlocal strategies are in cooperative games with imperfect information, such as multi-prover interactive proof systems. This paper develops a new method for proving limits of nonlocal strategies that make use of prior entanglement among players (or, provers, in the terminology of multi-prover interactive proofs). Instead of proving the limits for usual isolated provers who initially share entanglement, this paper proves the limits for "commuting-operator provers", who share private space, but can apply only such operators that are commutative with any operator applied by other provers. Obviously, these commuting-operator provers are at least as powerful as usual isolated but prior-entangled provers, and thus, limits in the model with commuting-operator provers immediately give limits in the usual model with prior-entangled provers. Using this method, we obtain an n-party generalization of the Tsirelson bound for the Clauser-Horne-Shimony-Holt inequality, for every n. Our bounds are tight in the sense that, in every n-party case, the equality is achievable by a usual nonlocal strategy with prior entanglement. We also apply our method to a three-prover one-round binary interactive proof system for NEXP. Combined with the technique developed by Kempe, Kobayashi, Matsumoto, Toner and Vidick to analyze the soundness of the proof system, it is proved to be NP-hard to distinguish whether the entangled value of a three-prover one-round binary-answer game is equal to one or at most 1-1/p(n) for some polynomial p, where n is the number of questions. This is in contrast to the two-prover one-round binary-answer case, where the corresponding problem is efficiently decidable. Alternatively, NEXP has a three-prover one-round binary interactive proof system with perfect completeness and soundness 1 middot $2^{-poly}.$
Starting Page	187
Ending Page	198
File Size	456492
Page Count	12
File Format	PDF
ISBN	9780769531694
ISSN	10930159
DOI	10.1109/CCC.2008.12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-06-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Computational complexity Informatics Computer science Sun Quantum mechanics Information theory Terminology Educational programs Educational technology Indium tin oxide Tsirelson inequality multi-prover interactive proof systems quantum nonlocality entanglement
Content Type	Text
Resource Type	Article

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Generalized tsirelson inequalities, commuting-operator provers, and multi-prover interactive proof systems (2008)

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