标题： 宏观量子相干性和机械系统中的纠缠 显示英文标题

标题： Macroscopic quantum coherence and entanglement in mechanical systems

摘要： 宏观量子态的概念必须明确，以便评估实验在多大程度上探测了量子力学的大尺度极限。 然而，量化所谓的量子宏观性的议题存在多种方法，这些方法有不同的解释以及计算和测量的难易程度。 在这里，我们引入两种度量，以捕捉独立的宏观特性：i) 广延尺寸，衡量位置或动量可观测量相对于原子尺度单位的相干程度，以及 ii) 纠缠尺寸，量化纠缠子系统的数量。 这些度量结合了许多以往提议中 desirable 的特性，并且从量子信息理论的角度出发，以相干性和多体纠缠为基础，具有严格合理的解释。 我们展示了如何利用微机械振荡器和衍射分子的实验数据来估计它们并获得下限。 值得注意的是，我们在最近的机械叠加态中发现了$10^6$到$10^7$个原子的真实多体纠缠的证据。 显示英文摘要

摘要： The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of $10^6$ to $10^7$ atoms in recent mechanical superposition states.