Entanglers in 3-strategies ELW games

TL;DR

This paper develops a general quantum gate operator for two-player three-strategy ELW games using SU(3) algebra, analyzing how entanglement relates to the stability of initial states.

Contribution

It introduces a construction of the general gate operator for 3-strategy ELW games based on Cartan subalgebra of SU(3), linking entanglement to state stability.

Findings

Gate operator constructed from SU(3) Cartan subalgebra

Relation established between entanglement and stability subgroup

Framework for analyzing multi-strategy quantum games

Abstract

We construct the general gate operator for 2-players 3-strategies ELW games. It is shown that such a gate, implementing classical strategies, can be constructed out of the elements of Cartan subalgebra of $SU(3)$. The relation between the degree of entanglement and the structure of stability subgroup of initial state is analyzed.