Gaming the Quantum

TL;DR

This paper clarifies the distinction between two perspectives of quantum game theory, providing a proper description of quantum games and linking Nash equilibria to quantum state approximations, with implications for quantum information systems.

Contribution

It delineates the two perspectives of quantum game theory and offers a proper framework for quantum games, connecting Nash equilibria to quantum state approximation problems.

Findings

Nash equilibrium in quantum games corresponds to a best approximation in quantum state space.

Provides a formal framework for quantum games rooted in game theory.

Links quantum game equilibria to behaviors of quantum physical systems.

Abstract

In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of "quantized games", and of applying game theory to quantum mechanics, referred to henceforth as "gaming the quantum", have become synonymous under the single ill-defined term "quantum game". Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multi-player, non-cooperative game quantum mechanical, is given. Within the context of this description, finding a Nash equilibrium in a strictly competitive quantum game is shown to be equivalent to finding a solution to a simultaneous best approximation problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of "equilibrium" behavior of quantum physical systems such as those utilized in quantum information processing and computation.