skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Duality, phase structures, and dilemmas in symmetric quantum games

Abstract

Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD, and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of the players are provided.

Authors:
 [1];  [2]
  1. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan). E-mail: tsubasa@post.kek.jp
  2. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan)
Publication Date:
OSTI Identifier:
20976734
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 3; Other Information: DOI: 10.1016/j.aop.2006.05.001; PII: S0003-4916(06)00110-2; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DUALITY; GAME THEORY; HILBERT SPACE; MATRICES; QUANTIZATION; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS

Citation Formats

Ichikawa, Tsubasa, and Tsutsui, Izumi. Duality, phase structures, and dilemmas in symmetric quantum games. United States: N. p., 2007. Web. doi:10.1016/j.aop.2006.05.001.
Ichikawa, Tsubasa, & Tsutsui, Izumi. Duality, phase structures, and dilemmas in symmetric quantum games. United States. doi:10.1016/j.aop.2006.05.001.
Ichikawa, Tsubasa, and Tsutsui, Izumi. Thu . "Duality, phase structures, and dilemmas in symmetric quantum games". United States. doi:10.1016/j.aop.2006.05.001.
@article{osti_20976734,
title = {Duality, phase structures, and dilemmas in symmetric quantum games},
author = {Ichikawa, Tsubasa and Tsutsui, Izumi},
abstractNote = {Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD, and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of the players are provided.},
doi = {10.1016/j.aop.2006.05.001},
journal = {Annals of Physics (New York)},
number = 3,
volume = 322,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of Z{sub N} models in the N{yields}{infinity} limit. Two phase transitions featuring a fixed line are shown to appear inmore » the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.« less
  • The electronic states and carrier transport in (100)PbTe/Pb {sub 1-x} Eu{sub x} Te double quantum wells are theoretically analyzed. The dependences of the mobility and Seebeck coefficient on the thickness of the internal barrier in symmetric and asymmetric structures are investigated. It was found that at great distance between the wells even small violation of the structure symmetry and essential reconstruction of electron wave functions results in suppression of intersubband scattering with carriers transfer between the wells and provides the correct limit to isolated quantum well in kinetic coefficients. Some possibilities of increasing the thermoelectric power factor are found, andmore » a suitable set of structure parameters is calculated within the proposed model.« less
  • A Comment on the Letter by Jens Eisert, Martin Wilkens, and Maciej Lewenstein, Phys.Rev.Lett. 83, 3077 (1999). The authors of the Letter offer a Reply.
  • Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called duality quantum computingmore » mode. The quantum particle-wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.« less
  • We show that quantum games are more efficient than classical games and provide a saturated upper bound for this efficiency. We also demonstrate that the set of finite classical games is a strict subset of the set of finite quantum games. Our analysis is based on a rigorous formulation of quantum games, from which quantum versions of the minimax theorem and the Nash equilibrium theorem can be deduced.