Quantum measurements designed for safer decisions in risky settings
Risk-Averse Decision Making via Quantum Measurement Design
Information Theory
Summary
When quantum measurements guide decisions, just focusing on average results can hide the risk of bad outcomes. The authors find a way to design quantum measurements that care about these risks using a concept called optimized certainty equivalent, which includes popular risk measures like conditional value at risk. They show that for certain types of gain functions, the problem can be turned into a manageable set of mathematical programs, and give a neat formula for picking between two states. Their tests show these smart measurements reduce the chance of very bad results while only slightly lowering average performance.
What this means in practice
- •For quantum communication engineers: Create quantum measurements that reduce worst-case losses in protocols by optimizing risk-sensitive objectives rather than just average success.
- •For financial risk modelers: Incorporate quantum-inspired decision tools that prioritize risk-averse strategies when outcomes depend on quantum state measurements.
Authors
Meiyi Zhu, Osvaldo Simeone
Abstract
Quantum measurements are conventionally optimized to maximize the average of a utility that depends on the true state and on the measurement outcome. However, when the outcome of the measurement is used as an action within a larger decision-making system, the average utility does not capture the risk of poor outcomes. This letter addresses the design of quantum measurements that maximize a risk-averse objective given by the optimized certainty equivalent (OCE), a family of criteria that includes the average utility and the conditional value at risk (CVaR) as special cases. For a piecewise linear gain function, defining the OCE, thus including the CVaR, the problem is shown to reduce to a finite number of semidefinite programs, for which a dual formulation is derived. For the discrimination of two states, a closed-form solution is obtained that takes the form of a Helstrom measurement. Numerical results show that the optimized measurement improves the lower tail of the utility distribution at a moderate cost in average utility.