Entangled N-photon states for fair and optimal social decision making

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

doi:10.1038/s41598-020-77340-3

Abstract

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. In these respects, the intrinsic randomness and global properties of quantum states provide ideal tools for obtaining optimal solutions to this problem. Based on the previous study of the CMAB problem in the two-arm, two-player case, this paper presents the theoretical principles necessary to find polarization-entangled N-photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Although a general formula for the N-player case is not presented here, general derivation rules and a verification algorithm are proposed. This report demonstrates the potential usability of quantum states in collective decision making with limited, probabilistic resources, which could serve as a first step toward quantum-based resource allocation systems.

Highlights

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals
The multi-arm bandit (MAB) problem is a typical example of decision making inspired by game theory, in which a user faces several choices with identical potential reward amounts, whose reward probabilities are unknown to the user but can change without notice
We extended this work to the use of N polarized photons in an N-photon quantum superposition state to solve the CMAB in more general situations with N ≥ 2 and two choices

Summary

Introduction

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. Based on the previous study of the CMAB problem in the twoarm, two-player case, this paper presents the theoretical principles necessary to find polarizationentangled N-photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Using already established a lgorithms[18], these works have demonstrated the potential usability of physics to solve complex decision-making situations efficiently, in up to a 64-arm single-user case[13]

Results

Discussion

Conclusion