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

ArXiv ID: 2308.01305 “View on arXiv”

Authors: Unknown

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.

Keywords: Quantum Finance, Portfolio Optimization, Kelly Criterion, Quantum Measurement, Information Theory, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced quantum probability, density matrices, and backward induction optimization, which is mathematically dense. However, it is a theoretical study with numerical simulations on a toy model, lacking real financial data, backtests, or implementation details for trading.

  flowchart TD
    A["Research Goal:<br/>Find optimal quantum betting strategy<br/>for spin-1/2 particles"] --> B{"Data/Inputs:<br/>Sequence of spin-1/2 particles<br/>Initial wealth & betting fractions"}
    B --> C["Methodology: Numerical Optimization"]
    C --> D["Computational Process:<br/>Iteratively adjust measurement directions<br/>to maximize portfolio growth rate"]
    D --> E{"Comparison"}
    E --> F["Classical Strategy:<br/>Kelly Criterion"]
    E --> G["Optimal Quantum Strategy"]
    F --> H["Findings:<br/>Quantum strategy outperforms classical<br/>Extension of portfolio optimization<br/>to quantum realm"]
    G --> H