Quantum games and quantum algorithms

TL;DR

This paper explores the connection between quantum algorithms and quantum game strategies, demonstrating how quantum advantages can be achieved in certain oracle problems, including the Bernstein-Vazirani algorithm which operates without entanglement.

Contribution

It formalizes the relationship between quantum algorithms and game theory, providing examples where quantum strategies outperform classical ones, notably in the Bernstein-Vazirani problem.

Findings

Quantum strategies can outperform classical strategies in certain oracle problems.

The Bernstein-Vazirani algorithm creates no entanglement during its execution.

The paper establishes a formal link between quantum algorithms and game theory.

Abstract

A quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalize this correspondence and give examples of games (and hence oracle problems) for which the quantum player can do better than would be possible classically. The most remarkable example is the Bernstein-Vazirani quantum search algorithm which I show creates no entanglement at any timestep.