Risk-Averse Decision Making via Quantum Measurement Design

2026-09-09

AI Summary

本文针对决策系统中的风险规避问题，通过设计量子测量来最大化优化确定等价（OCE），并对于两种状态的区分给出了闭式解。

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.

Problem

• Risk-Averse Decision Making
• Quantum Measurement Design
• Optimized Certainty Equivalent (OCE)
• Conditional Value at Risk (CVaR)

Innovation

• optimized certainty equivalent (OCE)
• risk-averse decision making
• quantum measurement design
• semidefinite programming
• Helstrom measurement