Conflict-free collective stochastic decision making by orbital angular momentum of photons through quantum interference

TL;DR

This paper introduces a scalable quantum decision-making method using the orbital angular momentum of photons, enabling conflict-free multi-armed bandit solutions with high-dimensional choices and quantum interference effects.

Contribution

It proposes a novel approach leveraging orbital angular momentum of photons for scalable, conflict-free decision-making in multi-armed bandit problems, extending quantum interference techniques.

Findings

Achieves near-maximum total rewards in three-armed bandit simulations.

Demonstrates conflict-free decision-making using quantum interference.

Extends Hong-Ou-Mandel effect to multiple states for multi-photon generation.

Abstract

In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.