Transfer of quantum game strategies

TL;DR

This paper presents a method for transferring perfect strategies between different classes of two-player quantum non-local games using operator space isomorphisms, with implications for quantum game theory.

Contribution

It introduces a novel approach for strategy transfer based on quantum homomorphisms and characterizes new classes of correlations relevant for quantum game strategies.

Findings

Strategy transfer is possible via operator space isomorphisms.

Characterization of new QNS correlations in terms of tensor product states.

Introduction of jointly tracial correlations related to ${ m C}^{*}$-algebras.

Abstract

We develop a method for the transfer of perfect strategies between various classes of two-player, one round cooperative non-local games with quantum inputs and outputs using the simulation paradigm in quantum information theory. We show that such a transfer is possible when canonically associated operator spaces for each game are quantum homomorphic or isomorphic, as defined in the joint work of H. and Todorov (2024). We examine a new class of QNS correlations, needed for the transfer of strategies between games, and characterize them in terms of states on tensor products of canonical operator systems. We define jointly tracial correlations and show they correspond to traces acting on tensor products of canonical ${\rm C}^{*}$-algebras associated with individual game parties. We then make an inquiry into the initial application of such results to the study of concurrent quantum games.