A three-player coherent state embezzlement game

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 $0<c\le 1$ such that to succeed with probability $1-\epsilon$ in the game it is necessary to use an entangled state of at least $\Omega ({\epsilon }^{-c})$ qubits, and it is sufficient to use a state of at most $O({\epsilon }^{-1})$ 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 $C^{\ast }$-algebras respectively.

arXiv commentVersion published in Quantum

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Cited by in corpus (2)

• Complete Characterization of Entanglement Embezzlement
• Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement