发表机构
National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子到经典测量的充分性概念，通过因子分解准则识别典型测量，将量子统计决策问题精确简化为经典问题，并应用于谱推断和位移热态参数估计。
AI 中文摘要
量子测量将量子统计实验转化为经典实验，但不同的测量通常会产生具有不同统计信息的实验。我们引入了量子到经典的充分性：相对于一个规定的测量类，如果一个测量诱导的经典实验在Blackwell意义上支配该类中所有其他测量的实验，则该测量是充分的。这分离了量子推断的两个组成部分：通过对称性或决策论论证减少测量类，以及通过实验层面的充分性条件在减少的类中识别一个典型测量。我们建立了一个因子分解准则，其中参数仅通过正交块分解的权重进入群平均实验。那么，块标签测量相对于所有不变测量是充分的。对于酉共轭下的张量积模型，这识别了弱Schur采样作为谱推断的充分测量。结合保风险对称化，它将所有测量上的不变贝叶斯和极小极大问题精确地简化为基于Young图的经典决策问题。我们推导了光滑谱泛函的尖锐一阶渐近贝叶斯和极小极大风险。我们在连续变量设置中为非紧致群作用建立了类似的简化。我们考虑了位移热态和热参数泛函，其中位移未知。在位移不变测量内，总残余光子数测量作为充分测量出现。结合Hunt-Stein约简，这产生了所有测量上的贝叶斯极小极大和极小极大问题的精确有限样本简化，简化为基于总残余光子数的经典决策问题，该光子数遵循负二项分布。
英文摘要
A quantum measurement transforms a quantum statistical experiment into a classical one, but different measurements generally yield experiments with different statistical information. We introduce quantum-to-classical sufficiency: relative to a prescribed measurement class, a measurement is sufficient if its induced classical experiment Blackwell-dominates those from every other measurement in the class. This separates two components of quantum inference: reducing the measurement class through symmetry or decision-theoretic arguments, and identifying a canonical measurement in the reduced class by an experiment-level sufficiency condition. We establish a factorization criterion where the parameter enters the group-averaged experiment only through weights of an orthogonal block decomposition. The block-label measurement is then sufficient relative to all invariant measurements. For tensor-product models under unitary conjugation, this identifies weak Schur sampling as the sufficient measurement for spectral inference. Combined with risk-preserving symmetrization, it reduces invariant Bayes and minimax problems over all measurements exactly to classical decision problems based on Young diagrams. We derive sharp first-order asymptotic Bayes and minimax risks for smooth spectral functionals. We establish an analogous reduction for a noncompact group action in a continuous-variable setting. We consider displaced thermal states and functionals of the thermal parameter with an unknown displacement. Within displacement-invariant measurements, total residual photon number measurement emerges as the sufficient measurement. Combined with Hunt-Stein reduction, this yields exact finite-sample reductions of Bayes-minimax and minimax problems over all measurements to classical decision problems based on the total residual photon count, which follows a negative binomial distribution.
Comments78 pages
