Entangled and correlated photon mixed strategy for social decision making

Shion Maeda,Serge Huant,Guillaume Bachelier,Nicolas Chauvet,Makoto Naruse,Hayato Saigo,Hirokazu Hori

doi:10.1038/s41598-021-84199-5

Abstract

Collective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.

Highlights

Conflicts are avoided and maximum total reward is accomplished while ensuring equality[16]
To accommodate the aforementioned changes in the environmental conditions and maximize total rewards, we propose and demonstrate a mixed strategy of utilizing entangled photons and classical photons to find the optimal solution of 2-player, 2-armed bandit problems
We show that an optimal mixture of entangled and correlated photons exists depending on the dynamics of the reward environment as well as the difficulty of finding the higher reward probability machine

Summary

Introduction

Conflicts are avoided and maximum total reward is accomplished while ensuring equality[16]. We showed that classical photons, in the sense of not-entangled states such as single photons and correlated photon pairs, cannot resolve decision conflicts[16]. In these studies, the reward dispensed from a slot machine is constant at a time. To accommodate the aforementioned changes in the environmental conditions and maximize total rewards, we propose and demonstrate a mixed strategy of utilizing entangled photons and classical photons (polarization-entangled photon pairs and polarization-correlated photon pairs) to find the optimal solution of 2-player, 2-armed bandit problems. When recognizing that the conflicted choice provides greater rewards, we utilize correlated photons to fully exploit the reward from the environment. The following discussion is restricted to 2-player, 2-choice problems, the present study captures the essential aspects of entangled and classical-photon mixed strategies that can be extended for solving more generalized problems

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Results

Discussion

Conclusion