Extended non-local games and monogamy-of-entanglement games.
We study a generalization of non-local games-which we callextended 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 themonogamy-of-entanglementgames 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 Tomamichelet al.concerning monogamy-of-entanglement games.
Department 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.
Nathaniel
N
Johnston
Department of Computer Science and Engineering , IIT Kanpur , Kanpur, Uttar Pradesh 208016, India.
Rajat
R
Mittal
Institute for Quantum Computing, School of Computer Science, University of Waterloo , Waterloo, Ontario, Canada N2L 3G1.
Vincent
0000-0002-8952-8981
V
Russo
Institute for Quantum Computing, School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8.
John
J
Watrous
extended non-local games; monogamy-of-entanglement; non-local games; quantum steering; semidefinite programming