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The HoneyComb Paradigm for Research on Collective Human Behavior
Published on: January 19, 2019
Extended non-local games and monogamy-of-entanglement games
Nathaniel Johnston1, Rajat Mittal2, Vincent Russo3
1Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada E4L 1E4; Institute for Quantum Computing, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1.
Abstract:
We study a generalization of non-local games-which we call extended non-local games-in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on the outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski and Wehner, which they also generalize. We prove that a natural extension of the Navascués-Pironio-Acín hierarchy of semidefinite programmes converges to the optimal commuting measurement value of extended non-local games, and we prove two extensions of results of Tomamichel et al. concerning monogamy-of-entanglement games.
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