Risk-Averse Decision Making via Quantum Measurement Design
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.
Related
- Risk-Averse Decision Making with Multi-Level Reliability Guarantees
- Conformal Risk-Averse Decision Making with Optimized Certainty Equivalent Risk Control
- Credal Machine Learning for Risk-Averse Decision Making
- Risk-averse design optimization with CVaR constraints via multifidelity tail-region correction
- Classes of Aggregation Rules for Ethical Decision Making in Automated Systems
BibTeX
@misc{zhu2026riskaverse,
title = {{Risk-Averse Decision Making via Quantum Measurement Design}},
author = {Meiyi Zhu and Osvaldo Simeone},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10482},
eprint = {2609.10482},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10482},
}
RIS
TY - UNPB
TI - Risk-Averse Decision Making via Quantum Measurement Design
AU - Meiyi Zhu
AU - Osvaldo Simeone
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10482
UR - https://arxiv.org/abs/2609.10482
AB - 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.
ER -