Abstract
The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of “quantum advantages” in various information processing tasks. Problems such as when quantum advantage exists, and if existing, how much it could be, are at a central position of these studies. In a broad class of scenarios, there are, implicitly or explicitly, at least two parties involved, who share a state, and the correlation in this shared state is the key factor to the efficiency under concern. In these scenarios, the shared entanglement or discord is usually what accounts for quantum advantage. In this paper, we examine a fundamental problem of this nature from the perspective of game theory, a branch of applied mathematics studying selfish behaviors of two or more players. We exhibit a natural zero-sum game, in which the chance for any player to win the game depends only on the ending correlation. We show that in a certain classical equilibrium, a situation in which no player can further increase her payoff by any local classical operation, whoever first uses a quantum computer has a big advantage over its classical opponent. The equilibrium is fair to both players and, as a shared correlation, it does not contain any discord, yet a quantum advantage still exists. This indicates that at least in game theory, the previous notion of discord as a measure of non-classical correlation needs to be reexamined, when there are two players with different objectives.
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Notes
- 1.
Note that there is also a class of “nonlocal games”, such as CHSH or GHZ games [BCMdW10], where all the players have the same objective. But general game theory focuses more on situation that the players have different objective functions, and the players are selfish, each aiming to optimize her own objective function only.
- 2.
A game is \([-1,1]\)-normalized if all utility functions have ranges within \([-1,1]\).
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Acknowledgments
Z.W. thanks Leong Chuan Kwek and Luming Duan for helpful comments. Z.W. was supported by the Singapore National Research Foundation under NRF RF Award No. NRF-NRFF2013-13 and the WBS grant under contract no. R-710-000-007-271. S.Z. was supported by Research Grants Council of the Hong Kong (Project no. CUHK419011, CUHK419413), and this research benefited from visits to Tsinghua University partially supported by China Basic Research Grant 2011CBA00300 (sub-project 2011CBA00301) and to Centre for Quantum Technologies partially under their support.
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Wei, Z., Zhang, S. (2015). Quantum Game Players Can Have Advantage Without Discord. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_27
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