通过量子测量设计实现风险规避决策
Risk-Averse Decision Making via Quantum Measurement Design
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中文总结 AI 辅助
本文提出通过优化确定性等价设计量子测量以实现风险规避决策，将问题简化为半定规划并给出闭式解，在适度牺牲平均效用下改善下尾风险。
中文摘要 AI 辅助
量子测量通常被优化以最大化依赖于真实状态和测量结果的效用的平均值。然而，当测量结果在更大的决策系统中被用作行动时，平均效用并不能捕捉到不良结果的风险。本文探讨了量子测量的设计，旨在最大化由优化确定性等价（OCE）给出的风险规避目标，OCE是一系列准则，其中包括平均效用和条件风险价值（CVaR）作为特例。对于定义OCE的分段线性增益函数，因此包括CVaR，该问题被证明可简化为有限数量的半定规划，并推导出其对偶形式。对于两个态的判别，获得了闭式解，其形式为Helstrom测量。数值结果表明，优化后的测量以平均效用的适度成本改善了效用分布的下尾。
英文摘要
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.
发表机构
- King’s College London（伦敦国王学院）
- Northeastern University London（伦敦东北大学）
机构由 AI 辅助整理，请以论文原文为准。
