1Centre for Quantum Software and Information, University of Technology Sydney, Australia
2University of Waterloo and the Perimeter Institute, Canada. Email: textttwcleung@uwaterloo.ca
3California Institute of Technology, USA. Email: textttvidick@cms.caltech.edu
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Abstract
We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of $1$ in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant $0 <cleq 1$ such that to succeed with probability $1-varepsilon $ in the game it is necessary to use an entangled state of at least $Omega(varepsilon ^{-c})$ qubits, and it is sufficient to use a state of at most $O(varepsilon ^{-1})$ qubits.
The game is based on the coherent state exchange game of Leung et al. (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al. (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of finitely presented groups and $C^*$-algebras respectively.
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Cited by
[1] Andrea Coladangelo and Jalex Stark, “Unconditional separation of finite and infinite-dimensional quantum correlations”, arXiv:1804.05116.
[2] Joseph Fitzsimons, Zhengfeng Ji, Thomas Vidick, and Henry Yuen, “Quantum proof systems for iterated exponential time, and beyond”, arXiv:1805.12166.
[3] Oded Regev and Thomas Vidick, “Bounds on Dimension Reduction in the Nuclear Norm”, arXiv:1901.09480.
[4] Andrea Coladangelo, “A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations”, arXiv:1904.02350.
[5] William Slofstra, “A group with at least subexponential hyperlinear profile”, arXiv:1806.05267.
[6] Richard Cleve, Benoit Collins, Li Liu, and Vern Paulsen, “Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement”, arXiv:1811.12575.
[7] Louis Mathieu and Mehdi Mhalla, “Separating pseudo-telepathy games and two-local theories”, arXiv:1806.08661.
[8] Andrea Coladangelo and Jalex Stark, “An inherently infinite-dimensional quantum correlation”, Nature Communications 11, 3335 (2020).
The above citations are from SAO/NASA ADS (last updated successfully 2020-10-28 11:02:16). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2020-10-28 11:02:14).
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Source: https://quantum-journal.org/papers/q-2020-10-26-349/
