论文标题
曲面上的纠缠：一种野外策略的方法
Entanglement on curved hypersurfaces: A field-discretizer approach
论文作者
论文摘要
我们提出了一个协变方案，用于测量相对论量子场理论中一般性突出的纠缠。为此，我们介绍了一个辅助相对论领域“离散器”，该领域通过沿着高表面与该领域进行局部交互，完全交换了该领域的和离散器的状态。可以证明，可以使用离散器以协变的方式有效地截止该领域的无限态度，而无需引入空间晶格。反过来，这为我们提供了一种评估任意区域的纠缠的有效方法。作为示例，我们研究了1+1个维度的互补区和分离区域之间的纠缠，Minkowski空间中的平坦超曲面，米尔恩空间中的弯曲超曲面以及接近无效表面表面的高空丘脑区域。我们的结果表明，在1+1个维度中，任意超曲面的区域之间的纠缠仅取决于区域的时空终点，而不取决于内部的形状。我们的结果证实并扩展了扁平曲面的先前结果。
We propose a covariant scheme for measuring entanglement on general hypersurfaces in relativistic quantum field theory. For that, we introduce an auxiliary relativistic field, 'the discretizer', that by locally interacting with the field along a hypersurface, fully swaps the field's and discretizer's states. It is shown, that the discretizer can be used to effectively cut-off the field's infinities, in a covariant fashion, and without having to introduce a spatial lattice. This, in turn, provides us an efficient way to evaluate entanglement between arbitrary regions on any hypersurface. As examples, we study the entanglement between complementary and separated regions in 1+1 dimensions, for flat hypersurfaces in Minkowski space, for curved hypersurfaces in Milne space, and for regions on hypersurfaces approaching null-surfaces. Our results show that the entanglement between regions on arbitrary hypersurfaces in 1+1 dimensions depends only on the space-time endpoints of the regions, and not on the shape of the interior. Our results corroborate and extend previous results for flat hypersurfaces.
