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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.
Proceedings. Mathematical, Physical, and Engineering Sciences
|June 10, 2016
Summary
We introduce extended non-local games, a generalization of quantum games where a referee
Area of Science:
- Quantum Information Theory
- Quantum Game Theory
- Quantum Computing
Background:
- Non-local games are a key concept in quantum information theory.
- Existing frameworks do not fully capture scenarios involving referee measurements.
- Monogamy-of-entanglement games inspired this generalization.
Purpose of the Study:
- To introduce and study extended non-local games.
- To generalize existing non-local and monogamy-of-entanglement games.
- To analyze the computational complexity and optimal strategies in these new games.
Main Methods:
- Generalization of non-local game definitions.
- Extension of the Navascués-Pironio-Acín hierarchy.
- Analysis of semidefinite programming hierarchies.
Main Results:
- A natural extension of the Navascués-Pironio-Acín hierarchy converges to the optimal commuting measurement value.
- Two extensions of monogamy-of-entanglement game results are proven.
- The study establishes a computable upper bound for extended non-local games.
Conclusions:
- Extended non-local games provide a richer framework for studying quantum correlations.
- The developed hierarchy offers a powerful tool for analyzing these games.
- This work advances the understanding of quantum game theory and its applications.
Keywords:
extended non-local gamesmonogamy-of-entanglementnon-local gamesquantum steeringsemidefinite programmingMore Related Videos
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