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

TL;DR

This paper explores how entangled N-photon quantum states can be used to optimize resource allocation and fairness in multi-player decision-making scenarios modeled by the CMAB problem, demonstrating potential quantum advantages.

Contribution

It develops theoretical principles and numerical methods for using polarization-entangled N-photon states to optimize total output and fairness in multi-player resource allocation, extending previous two-player work.

Findings

Quantum states can optimize resource output and fairness.

Numerical simulations validate strategies for 2-5 players.

Verification algorithms assist in multi-player configuration.

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.