Synthesizing the Born rule with reinforcement learning

TL;DR

This paper explores how a reinforcement learning agent can approximate the Born rule from quantum mechanics by simulating decision-making and analyzing deviations, with potential experimental validation using single photons.

Contribution

It introduces a reinforcement learning framework to model deviations from the Born rule and proposes an experimental setup with single photons to test the theory.

Findings

Reinforcement learning can approximate the Born rule in decision-making.

Deviations from the Born rule depend on the agent’s learning parameters.

Experimental implementation with heralded single photons is feasible.

Abstract

According to the subjective Bayesian interpretation of quantum theory (QBism), quantum mechanics is a tool that an agent would be wise to use when making bets about natural phenomena. In particular, the Born rule is understood to be a decision-making norm, an ideal which one should strive to meet even if usually falling short in practice. What is required for an agent to make decisions that conform to quantum mechanics? Here we investigate how a realistic (hence non-ideal) agent might deviate from the Born rule in its decisions. To do so we simulate a simple agent as a reinforcement-learning algorithm that makes `bets' on the outputs of a symmetric informationally-complete measurement (SIC) and adjusts its decisions in order to maximize its expected return. We quantify how far the algorithm's decision-making behavior departs from the ideal form of the Born rule and investigate the limiting factors. We propose an experimental implementation of the scenario using heralded single photons.