Mini-maximizing two qubit quantum computations

TL;DR

This paper models two-qubit quantum computations as competitive games, establishing a link between game theory and quantum mechanics, and designs mechanisms to achieve optimal mini-max outcomes.

Contribution

It introduces a game-theoretic framework for two-qubit quantum computations and demonstrates the equivalence of Nash equilibrium and mini-max solutions in this context.

Findings

Nash equilibrium and mini-max outcomes are equivalent in two-qubit quantum games.

Quantum mechanisms can realize these mini-max outcomes.

The geometric structure of Hilbert space underpins the solution concepts.

Abstract

Two qubit quantum computations are viewed as two player, strictly competitive games and a game-theoretic measure of optimality of these computations is developed. To this end, the geometry of Hilbert space of quantum computations is used to establish the equivalence of game-theoretic solution concepts of Nash equilibrium and mini-max outcomes in games of this type, and quantum mechanisms are designed for realizing these mini-max outcomes.