标题： 量子场论中纠缠的普遍性如何？ 显示英文标题

标题： How ubiquitous is entanglement in quantum field theory?

摘要： 众所周知，纠缠在量子场论中是普遍存在的，具体来说：每个Reeh-Schlieder态都包含任意两个空间分离区域之间的纠缠。 这尤其适用于闵可夫斯基时空中的非相互作用标量理论的真空态。 关于场论中的纠缠讨论主要集中在包含无限多自由度的子系统上——通常是支持在一个空间紧致区域内的场模。 在本文中，我们研究了由有限多个场自由度组成的子系统中的纠缠，在$D+1$维闵可夫斯基时空中的自由标量理论中。 关注场的有限多个模是由真实实验的有限能力所驱动的。 我们发现有限维子系统之间的纠缠是{\em 完全不常见}，并且需要仔细选择模的支持区域才能显示出纠缠。 我们还发现高维空间中纠缠越来越稀疏。 我们得出结论，闵可夫斯基时空中的纠缠比通常认为的要少得多。 显示英文摘要

摘要： It is well known that entanglement is widespread in quantum field theory, in the following sense: every Reeh-Schlieder state contains entanglement between any two spatially separated regions. This applies, in particular, to the vacuum of a non-interacting scalar theory in Minkowski spacetime. Discussions on entanglement in field theory have focused mainly on subsystems containing infinitely many degrees of freedom -- typically, the field modes that are supported within a compact region of space. In this article, we study entanglement in subsystems made of finitely many field degrees of freedom, in a free scalar theory in $D+1$-dimensional Minkowski spacetime. The focus on finitely many modes of the field is motivated by the finite capabilities of real experiments. We find that entanglement between finite-dimensional subsystems is {\em not common at all}, and that one needs to carefully select the support of modes for entanglement to show up. We also find that entanglement is increasingly sparser in higher dimensions. We conclude that entanglement in Minkowski spacetime is significantly less ubiquitous than normally thought.