量子场的实空间纠缠
Real-space entanglement of quantum fields
摘要：
我们介绍了一种新的方法，允许分析确定的纠缠熵（和相关量）之间的配置的量子场，这是自由的或与经典源的相互作用，在两个不同的空间位置。我们展示了如何这样的设置可以描述一个二分的，连续的高斯系统。这使我们能够推导出明确的和精确的公式的纠缠熵，互信息和量子不和谐，仅在傅立叶空间功率谱的字段。这与以前的研究形成鲜明对比，以前的研究主要依赖于数值考虑。作为一个例子，我们应用我们的形式主义在平坦空间中的无质量场，在那里导出精确的表达式，只涉及该领域是粗粒度的区域的大小之间的比率，以及这些区域之间的距离。特别是，我们恢复了众所周知的事实，即互信息在大的距离衰减为该比率的四次方，如以前在数值计算中所观察到的。我们的方法导致了这个结果的第一个解析推导，并得到了一个也适用于任意距离的精确公式。最后，我们确定量子不和谐，并发现它同样消失（除非在涂抹的球体上进行粗粒化，在这种情况下，它在大距离上服从与互信息相同的抑制）。
英文摘要：
We introduce a new method permitting the analytical determination of entanglement entropy (and related quantities) between configurations of a quantum field, which is either free or in interaction with a classical source, at two distinct spatial locations. We show how such a setup can be described by a bipartite, continuous Gaussian system. This allows us to derive explicit and exact formulas for the entanglement entropy, the mutual information and the quantum discord, solely in terms of the Fourier-space power spectra of the field. This contrasts with previous studies, which mostly rely on numerical considerations. As an illustration, we apply our formalism to massless fields in flat space, where exact expressions are derived that only involve the ratio between the size of the regions over which the field is coarse-grained, and the distance between these regions. In particular, we recover the well-known fact that mutual information decays as the fourth power of this ratio at large distances, as previously observed in numerical works. Our method leads to the first analytical derivation of this result, and to an exact formula that also applies to arbitrary distances. Finally, we determine the quantum discord and find that it identically vanishes (unless coarse-graining is performed over smeared spheres, in which case it obeys the same suppression at large distance as mutual information).
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