作为N盒和量子鸽巢悖论资源的相干性
Coherence as a resource for $N$-box and quantum pigeonhole paradoxes
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中文总结 AI 辅助
研究涉及混合预选择和后选择状态的非逻辑PPS场景，以N盒和量子鸽巢悖论为例，通过证明悖论与单个特定算符的弱值异常及相干性的关联来分析，阐明非经典性概念作用及与经典解释的偏差。
中文摘要 AI 辅助
预选择和后选择（PPS）悖论是量子非经典性的显著例证。逻辑PPS悖论与背景性相关，其中用阿哈罗诺夫 - 伯格曼 - 莱博维茨（ABL）规则进行的推理恰好为0或1。非逻辑悖论缺乏这种强烈特征。本文分析了涉及混合预选择和后选择状态的更一般的非逻辑PPS场景。我们表明，N盒和量子鸽巢悖论这两种场景在中间测量的基础上需要预选择和后选择状态的相干性。通过证明每个悖论当且仅当存在单个特定于悖论的算符的弱值异常时成立，以及弱值异常需要相干性来实现这一点。这阐明了这些场景中不同非经典性概念的作用，突出了与量子理论的非相干子理论提供的（严格）经典解释所需的定量偏差。
英文摘要
Pre- and post-selection (PPS) paradoxes are striking demonstrations of quantum nonclassicality. Logical PPS paradoxes, where inferences made with the Aharonov-Bergmann-Lebowitz (ABL) rule are exactly 0 or 1, are linked to contextuality. Non-logical paradoxes lack this strong signature. In this work, we analyse more general, non-logical PPS scenarios involving mixed pre- and post-selected states. We show that two such scenarios, the $N$-box and quantum pigeonhole paradoxes, require coherence of both pre- and post-selected states in the basis of the intermediate measurement. This is done by showing each paradox holds if and only if there is weak-value anomaly for a single, paradox-specific operator, together with the fact that weak-value anomaly requires coherence. This clarifies the role of different notions of nonclassicality in these scenarios, highlighting the required quantitative departures from (strictly) classical explanations provided by incoherent sub-theories of quantum theory.
