Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1410.7706 · Quantum Information Processing

Note on maximally entangled Eisert–Lewenstein–Wilkens quantum games

Katarzyna Bolonek-Lasoń, Piotr Kosiński

Published Oct 22, 2015• 3 citations
arXivHTMLPDF

Abstract

Maximally entangled Eisert–Lewenstein–Wilkens games are analyzed. For a general class of gates defined in the previous papers of the first author, the general conditions are derived which allow to determine the form of gate leading to maximally entangled games. The construction becomes particularly simple provided one does distinguish between games differing by relabeling of strategies. Some examples are presented.

DOI
10.1007/s11128-015-1133-7

Related papers

Some properties of the maximally entangled Eisert-Wilkens-Lewenstein game

Katarzyna Bolonek-Lasoń, Piotr Kosiński

The Eisert–Wilkens–Lewenstein maximally entangled quantum game is studied within the framework of (elementary) group theory. It is shown that the game can be described in terms of a real Hilbert space of states. It is also shown that the crucial properties of the maximally entangled case, like quaternionic structure and the existence, for any given strategy, of the corresponding counterstrategy, result from the existence of a large stability subgroup of the initial state of the game.

arXiv:1209.2556•Progress of Theoretical and Experimental Physics•Jul 1, 2013•2 citations

General quantum two-player games, their gate operators, and Nash equilibria

Katarzyna Bolonek-Lasoń

Two-player |$N$|-strategy games quantized according to the Eisert–Lewenstein–Wilkens scheme [Phys. Rev. Lett. 83, 3077 (1999)] are considered. Group-theoretical methods are applied to the problem of finding a general form of gate operators (entanglers) under the assumption that the set of classical pure strategies is contained in the set of pure quantum ones. The role of the stability group of the initial state of the game is stressed. As an example, it is shown that maximally entangled games do not admit nontrivial pure Nash strategies. The general arguments are supported by explicit computations performed in the three-strategy case.

arXiv:1503.08851•Progress of Theoretical and Experimental Physics•Feb 23, 2015•10 citations

Quantum games

Jens Eisert, Martin Wilkens

In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.

•Jan 1, 2000•0 citations

Non-Classical Rules in Quantum Games

Piotr Frąckiewicz

Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players' strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme.

arXiv:2012.06915•Entropy•May 13, 2021•5 citations

On Nash equilibria in Eisert-Lewenstein-Wilkens game

Katarzyna Bolonek-Lasoń, Piotr Kosiński

Landsburg method of classifying mixed Nash equilibria for maximally entangled Eisert-Lewenstein-Wilkens (ELW) game is analyzed with special emphasis on symmetries inherent to the problem. Nash equilibria for the original ELW game are determined.

arXiv:1509.01843•Sep 6, 2015•0 citations

Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games

Piotr Frąckiewicz

The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form.

•Jan 1, 2016•2 citations
Maximally entangled Eisert–Lewenstein–Wilkens games are analyzed. For a general class of gates defined in the previous papers of the first author, the general conditions are derived which allow to determine the form of gate leading to maximally entangled games. The construction becomes particularly simple provided one does distinguish between games differing by relabeling of strategies. Some examples are presented.
Two-player |NNN|-strategy games quantized according to the Eisert–Lewenstein–Wilkens scheme [Phys. Rev. Lett. 83, 3077 (1999)] are considered. Group-theoretical methods are applied to the problem of finding a general form of gate operators (entanglers) under the assumption that the set of classical pure strategies is contained in the set of pure quantum ones. The role of the stability group of the initial state of the game is stressed. As an example, it is shown that maximally entangled games do not admit nontrivial pure Nash strategies. The general arguments are supported by explicit computations performed in the three-strategy case.
In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.
Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players' strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme.
The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form.