A quantum double-or-nothing game: The Kelly Criterion for Spins

TL;DR

This paper explores a quantum betting game involving spin-1/2 particles, demonstrating how quantum strategies can outperform classical ones in portfolio growth through adaptive measurement adjustments.

Contribution

It introduces a quantum version of the Kelly criterion for a spin-based betting game and numerically determines the optimal quantum strategy, extending portfolio optimization into quantum finance.

Findings

Quantum strategies differ from classical Kelly strategies.

Optimal quantum strategies enhance portfolio growth.

The approach advances quantum finance and decision-making.

Abstract

A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is accrued through astute betting. As information is gained from the stream of particles, the measurement directions are progressively adjusted, and the portfolio growth rate is raised. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy, which is associated with the Kelly criterion. The paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm.