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Entanglement of approximate quantum strategies in XOR games

Ostrev, Dimiter and Vidick, Thomas (2018) Entanglement of approximate quantum strategies in XOR games. Quantum Information and Computation, 18 (7-8). pp. 617-631. ISSN 1533-7146. http://resolver.caltech.edu/CaltechAUTHORS:20180926-101512002

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Abstract

We show that for any ε > 0 there is an XOR game G = G(ε) with Θ(ε^(−1/5)) inputs for one player and Θ(ε^(−2/5)) inputs for the other player such that Ω(ε^(−1/5)) ebits are required for any strategy achieving bias that is at least a multiplicative factor (1−ε) from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self-test for highly entangled states. Up to the exponent −1/5 the scaling of our bound with ε is tight: for any XOR game there is an ε-optimal strategy using ⌈ε^(−1)⌉ ebits, irrespective of the number of questions in the game.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.rintonpress.com/journals/qiconline.html#v18n78PublisherIssue Table of Contents
https://arxiv.org/abs/1609.01652arXivDiscussion Paper
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2018 Rinton Press. Research supported by NSF CAREER Grant CCF-1553477 and the IQIM, an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-1553477
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Record Number:CaltechAUTHORS:20180926-101512002
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180926-101512002
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89955
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Sep 2018 17:27
Last Modified:26 Sep 2018 17:27

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