AI 中文总结
研究玻恩概率的量子不相容性，通过非理想量子参考系测量发现概率不确定且不可约，基于脉冲零差检测提出量子光学实现，推动量子态概念扩展，对量子理论与广义相对论界面研究有重要意义。
AI 中文摘要
量子理论挑战了个体测量结果是预先确定且独立于测量背景的观点。然而，量子态本身——所有可能测量的概率目录——通常被假定为定义明确。我们认为，这一假设默认依赖于相对于理想的、资源无限的参考系进行测量。我们表明，当相对于非理想量子参考系进行测量时，概率本身变得不确定：即使在任意大量运行的极限情况下，相对频率可能仍不确定。从量子力学意义上讲，这种不确定性是不可约的，正如我们通过证明相对频率的贝尔型定理所表明的那样。我们还基于脉冲零差检测提出了这些关联测量的量子光学实现。我们的发现促使将量子态的概念扩展到受有限资源约束的领域。我们预计它们在量子理论与广义相对论的界面处特别相关，在那里时空有限区域内可用的资源和信息从根本上是有限的。
英文摘要
Quantum theory challenges the view that individual measurement outcomes are predefined and independent of the measurement context. Yet the quantum state itself -- the catalogue of probabilities for all possible measurements -- is usually assumed to be well defined. We argue that this assumption tacitly relies on measurements being performed relative to ideal, infinitely-resourceful reference frames. We show that, when measurements are made relative to non-ideal quantum reference frames, the probabilities themselves become indefinite: even in the limit of arbitrarily large number of runs, the relative frequencies may remain uncertain. The uncertainty is irreducible in a quantum-mechanical sense, as we show by proving a Bell-type theorem for relative frequencies. We further propose a quantum-optical implementation of these relational measurements based on pulsed homodyne detection. Our findings motivate an extension of the notion of the quantum state to regimes constrained by finite resources. We expect them to be especially relevant at the interface between quantum theory and general relativity, where the resources and information available in a bounded region of spacetime are fundamentally limited.
Comments18+13 pages, 3 figures
