Can quantum entanglement implement classical correlated equilibria?

2014 ◽  
Vol 14 (5&6) ◽  
pp. 493-516
Author(s):  
Alan Deckelbaum
Keyword(s):  
Quantum State ◽  
Complete Information ◽  
Impossibility Result ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Initial State ◽  
Equilibrium Distributions ◽  
Pure Quantum State ◽  
Correlated Equilibria ◽  
Classical Game

We ask whether players of a classical game can partition a pure quantum state to implement classical correlated equilibrium distributions. The main contribution of this work is an impossibility result: we provide an example of a classical correlated equilibrium that cannot be securely implemented without useful information leaking outside the system. We study the model where players of a classical complete information game initially share an entangled pure quantum state. Players may perform arbitrary local operations on their subsystems, but no direct communication (either quantum or classical) is allowed. We explain why, for the purpose of implementing classical correlated equilibria, it is desirable to restrict the initial state to be pure and to restrict communication. In this framework, we define the concept of pure quantum correlated equilibrium (PQCE) and show that in a normal form game, any outcome distribution implementable by a PQCE can also be implemented by a classical correlated equilibrium (CE), but that the converse is false. We extend our analysis to extensive form games, and compare the power of PQCE to extensive form classical correlated equilibria (EFCE) and immediate-revelation extensive form correlated equilibria (IR-EFCE).

Game Theory

2016 ◽  
Author(s):  
Cristina Bicchieri ◽  
Giacomo Sillari
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Evolutionary Game Theory ◽  
Repeated Games ◽  
Evolutionary Game ◽  
Complete Information ◽  
Decision Makers ◽  
Correlated Equilibrium ◽  
Extensive Form

Game theory aims to understand situations in which decision-makers interact strategically. Chess is an example, as are firms competing for business, politicians competing for votes, animals fighting over prey, bidders competing in auctions, threats and punishments in long-term relationships, and so on. In such situations, the outcome depends on what the parties do jointly. Decision-makers may be people, organizations, animals, or even genes. In this chapter, the authors review fundamental notions of game theory and their application to philosophy of science. In particular, Section 1 looks at games of complete information through normal and extensive form representations, introduce the notion of Nash equilibrium and its refinements. Section 2 touches on epistemic foundations and correlated equilibrium, and Section 3 examines repeated games and their importance for the analysis of altruism and cooperation. Section 4 deals with evolutionary game theory.

scholarly journals Coarse Correlation in Extensive-Form Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1934-1941
Author(s):  
Gabriele Farina ◽  
Tommaso Bianchi ◽  
Tuomas Sandholm
Keyword(s):  
Normal Form ◽  
Saddle Points ◽  
Solution Concept ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Rational Agents ◽  
Correlation Models ◽  
Correlated Equilibria ◽  
Special Case

Coarse correlation models strategic interactions of rational agents complemented by a correlation device which is a mediator that can recommend behavior but not enforce it. Despite being a classical concept in the theory of normal-form games since 1978, not much is known about the merits of coarse correlation in extensive-form settings. In this paper, we consider two instantiations of the idea of coarse correlation in extensive-form games: normal-form coarse-correlated equilibrium (NFCCE), already defined in the literature, and extensive-form coarse-correlated equilibrium (EFCCE), a new solution concept that we introduce. We show that EFCCEs are a subset of NFCCEs and a superset of the related extensive-form correlated equilibria. We also show that, in n-player extensive-form games, social-welfare-maximizing EFCCEs and NFCCEs are bilinear saddle points, and give new efficient algorithms for the special case of two-player games with no chance moves. Experimentally, our proposed algorithm for NFCCE is two to four orders of magnitude faster than the prior state of the art.

scholarly journals Decentralized No-regret Learning Algorithms for Extensive-form Correlated Equilibria (Extended Abstract)

2021 ◽  
Author(s):  
Andrea Celli ◽  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Nicola Gatti
Keyword(s):  
Normal Form ◽  
Private Information ◽  
Imperfect Information ◽  
Research Question ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Learning Dynamics ◽  
Extensive Form Games ◽  
Normal Form Games ◽  
Correlated Equilibria

The existence of uncoupled no-regret learning dynamics converging to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form games generalize normal-form games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and the presence of private information, correlation in extensive-form games possesses significantly different properties than in normal-form games. The extensive-form correlated equilibrium (EFCE) is the natural extensive-form counterpart to the classical notion of correlated equilibrium in normal-form games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device ({\em a.k.a.} mediator) must take into account the evolution of beliefs of each player as they make observations throughout the game. Due to this additional complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a long time. In this article, we settle that question by giving the first uncoupled no-regret dynamics which provably converge to the set of EFCEs in n-player general-sum extensive-form games with perfect recall. We show that each iterate can be computed in time polynomial in the size of the game tree, and that, when all players play repeatedly according to our learning dynamics, the empirical frequency of play after T game repetitions is guaranteed to be a O(T^-1/2)-approximate EFCE with high probability, and an EFCE almost surely in the limit.

scholarly journals Protocol for optically pumping AlH+ to a pure quantum state

2020 ◽  
Vol 22 (42) ◽  
pp. 24423-24430
Author(s):  
Panpan Huang ◽  
Schuyler Kain ◽  
Antonio G. S. de Oliveira-Filho ◽  
Brian C. Odom
Keyword(s):  
Quantum State ◽  
Laser Fields ◽  
Pure Quantum State ◽  
Hyperfine State

Three laser fields drive the population of AlH+ to a single hyperfine state.

INFLUENCE OF INTRINSIC DECOHERENCE ON THE ENTANGLEMENT BETWEEN TWO ATOMS IN TAVIS–CUMMINGS MODEL

2008 ◽  
Vol 06 (01) ◽  
pp. 167-179
Author(s):  
CHUAN-JIA SHAN ◽  
WEI-WEN CHENG ◽  
TANG-KUN LIU ◽  
YAN-XIA HUANG ◽  
HONG LI ◽  
...  
Keyword(s):  
Strong Coupling ◽  
Quantum State ◽  
Dipole Interaction ◽  
Entangled State ◽  
Entanglement Dynamics ◽  
Initial State ◽  
Intrinsic Decoherence ◽  
Dipole Coupling ◽  
Fock State

Considering the dipole–dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the Tavis–Cummings model with intrinsic decoherence have been investigated. The two-atom entanglement appears with periodicity without considering intrinsic decoherence. However, the intrinsic decoherence causes the decay of entanglement between two atoms, with the decrease of the intrinsic decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state, the dipole–dipole coupling intensity and the field in the Fock state. Meanwhile, the two-atom quantum state will stay forever in the maximal entangled state when the initial state is proper, even in the presence of intrinsic decoherence. Furthermore, the two atoms can generate maximal entangled state even if they are initially separated by adjusting the dipole–dipole interaction, the strong coupling can improve the value of entanglement.

Can Quantum Measurements Prevent Change?

2020 ◽  
pp. 166-184
Author(s):  
Gershon Kurizki ◽  
Goren Gordon
Keyword(s):  
Quantum State ◽  
High Probability ◽  
Quantum Measurements ◽  
Repeated Measurements ◽  
Quantum Zeno Effect ◽  
Initial State ◽  
Zeno Effect

In a strange dream, Henry is coherently transported towards his bride down the aisle. But just as a small portion of him arrives next to her, that portion disappears in a flash of light caused by a snapshot! Henry keeps trying to be united with his bride, but repeated snapshots cause Henry’s collapse to being far away from her. This dream illustrates the quantum Zeno effect (QZE): if a measurement collapses the quantum state with high probability to the initial state, then frequent repeated measurements can almost stop the change of the quantum state. Yet less frequent measurements cause the opposite, anti-Zeno effect (AZE), whereby change or decay increases. Thus, decay is controllable. These effects confirm Zeno’s argument that change is an illusion, as it is up to the observer to prevent or induce it by appropriate observation. The appendix to this chapter explains the QZE for coherent and decay processes.

scholarly journals Canonical Thermal Pure Quantum State

2013 ◽  
Vol 111 (1) ◽  
Author(s):  
Sho Sugiura ◽  
Akira Shimizu
Keyword(s):  
Quantum State ◽  
Pure Quantum State
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