标题： 子观测代数的熵和几何纠缠熵 显示英文标题

标题： Entropy of a subalgebra of observables and the geometric entanglement entropy

摘要： 处于真空态的量子场的几何纠缠熵已知是发散的，并且当正则化后，它会按区域边界的面积尺度变化。 在这里，我们引入了限制在某个区域内的真空态熵的一个操作性定义：考虑一个支持在该区域上并且具有有限分辨率的可观测量子代数。 然后我们定义这个子代数上状态的熵。 对于高斯态，例如自由标量场的真空态，我们讨论如何计算这种熵。 特别是，我们展示了对于球形区域，在子代数适当细化的情况下，我们恢复了一个面积定律。 显示英文摘要

摘要： The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the vacuum restricted to a region: we consider a subalgebra of observables that has support in the region and a finite resolution. We then define the entropy of a state restricted to this subalgebra. For Gaussian states, such as the vacuum of a free scalar field, we discuss how this entropy can be computed. In particular we show that for a spherical region we recover an area law under a suitable refinement of the subalgebra.