量化测量客观性：一种回溯预测方法
Quantifying Measurement Objectivity: A Retrodictive Approach
AI总结：
该研究针对量子测量结果何时可解读为揭示预先存在的客观属性的问题，提出基于量子测量回溯预测的定量方法，构造量化非客观性的双线性型并证明其分解性质，得出总非客观性在特定映射下不降低的结论。
AI中文摘要：
量子测量的结果何时可被解读为揭示了预先存在的客观属性？利用新近发展的量子测量回溯预测形式体系，我们对该问题进行了定量处理：对于任意POVM（正算子值测度）和忠实先验态，我们构造了一个半正定双线性型，该型通过每个实值结果特征的预测值与其回溯对应值之间的不一致，量化其非客观性。我们证明该型可精确分解为两个半正定双线性型之和：不清晰性型和由Wigner-Yanase斜信息给出的非对称性型。当且仅当结果特征相对于先验可被解读为揭示预先存在的属性时，该总型恰好为零；特别地，当且仅当POVM是清晰的且与先验对易时，该总型恒为零。最后，在保持先验且在其模群下协变的映射下，非对称性不会增加，且任何非对称性的损失至少被同等量的不清晰性抵消，因此总非客观性不会降低。
英文摘要：
When can one interpret the outcomes of a quantum measurement as revealing a pre-existing objective property? Using the recently developed formalism of quantum measurement retrodiction, we provide a quantitative treatment of this question: for any POVM and faithful prior state, we construct a positive semidefinite bilinear form that quantifies the non-objectivity of every real-valued outcome feature through the disagreement between its predictive value and its retrodictive counterpart. We show that this form decomposes exactly into the sum of two positive semidefinite bilinear forms: an unsharpness form and an asymmetry form given by Wigner--Yanase skew information. The total form vanishes precisely on those outcome features that can be interpreted, relative to the prior, as revealing pre-existing properties; in particular, it vanishes identically if and only if the POVM is sharp and commutes with the prior. Finally, under maps that preserve the prior and are covariant under its modular group, asymmetry cannot increase, and any loss of asymmetry is offset by at least as much unsharpness, so that total non-objectivity cannot decrease.
