Some properties of maximally entangled ELW game

TL;DR

This paper analyzes the properties of the maximally entangled ELW quantum game using group theory, revealing its quaternionic structure and the role of stability subgroups in strategy-counterstrategy relationships.

Contribution

It introduces a group-theoretic framework for understanding the maximally entangled ELW game and uncovers its quaternionic structure and stability subgroup properties.

Findings

The game can be described in a real Hilbert space of states.

Maximally entangled case exhibits quaternionic structure.

Existence of large stability subgroups relates strategies to counterstrategies.

Abstract

The Eisert et al. 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 real Hilbert space of states. It is also shown that the crucial properties of the maximally entangled case, like quaternionic structure and the existence, to any given strategy, the corresponding counterstrategy, result from the existence of large stability subgroup of initial state of the game.