Published June 18, 2020
| Version Published
Journal Article
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A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
Abstract
We describe a two-player non-local game, with a fixed small number of questions and answers, such that an ϵ-close to optimal strategy requires an entangled state of dimension 2^(Ω(ϵ−1/8)). Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick [17]. It reduces the number of players from three to two, as well as the question and answer set sizes. Moreover, it provides an (arguably) elementary proof of the non-closure of the set of quantum correlations, based on embezzlement and self-testing. In contrast, previous proofs [26,16,19] involved representation theoretic machinery for finitely-presented groups and C∗-algebras.
Additional Information
© 2020 Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. Published under CC-BY 4.0. The author thanks William Slofstra and Thomas Vidick for useful comments on an earlier version of this paper. The author also thanks the latter for helpful discussions. The author thanks Vern Paulsen for a useful email exchange about the game in [DPP17]. The author was supported by the Kortschak Scholars program and AFOSR YIP award number FA9550-16-1-0495.Attached Files
Published - q-2020-06-18-282.pdf
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q-2020-06-18-282.pdf
Additional details
Identifiers
- Eprint ID
- 104326
- Resolver ID
- CaltechAUTHORS:20200710-120957156
Related works
- Describes
- https://arxiv.org/abs/1904.02350 (URL)
Funding
- Kortschak Scholars Program
- Air Force Office of Scientific Research (AFOSR)
- FA9550-16-1-0495
Dates
- Created
-
2020-07-10Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field