Quantum Locality in Game Strategy

Carlos A Melo-Luna,John H Reina,Andrés F Ducuara,Astrid Barreiro,Cristian E Susa

doi:10.1038/srep44730

Carlos A Melo-Luna, John H Reina + Show 3 more

Open Access

https://doi.org/10.1038/srep44730

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Abstract

Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of novel game strategies that lead to new (quantum Nash) equilibrium points whereby players in some classical games are always outperformed if sharing and processing joint information ruled by the laws of quantum physics is allowed. We show that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players’ input states. This highlights the remarkable key role played by pure quantum coherence at powering some protocols. Finally, we propose an experiment that uses separable states and basic photon interferometry to demonstrate the locally-correlated quantum advantage.

Highlights

In 1944, von Neumann developed a formal framework of game theory[1], namely of understanding the dynamics of competition and cooperation between two or more competing parties that hold particular interests
2 ) input states; δ =π/2, and Purely local and/or separable input quantum states have been harnessed as a resource in the Prisoners’ Dilemma (PD) game, and we have shown that such a strategy gives a clear advantage over the original bipartite non-zero sum game that makes use of just classical resources
We have shown that neither entanglement nor any nonlocal property is strictly required at the input of the game in order to achieve a quantum (Q, Q ) strategy that removes the PD dilemma and outperforms any classical strategy

Summary

Introduction

In 1944, von Neumann developed a formal framework of game theory[1], namely of understanding the dynamics of competition and cooperation between two or more competing parties that hold particular interests In another seminal work, twenty years later, Bell discovered the intrinsic, fundamental nonlocal character of quantum theory[2], the fact that there exist quantumly correlated (entangled) particles whose measurement gives results that are impossible in classical physics—the so-called violation of Bell inequalities[3,4]. The interaction between players can be cast in a quantum circuit that generates, via the action of a two-qubit operator ˆ (δ), an initial state of the form: ψin(δ)

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