论文标题
关于图的量子叠加，无信号和协方差
On quantum superpositions of graphs, no-signalling and covariance
论文作者
论文摘要
我们在数学上和概念上提供了图形量子叠加的强大概念。我们认为，在至关重要的情况下，图形的量子叠加需要节点名称以使其正确的对齐方式，我们通过无信号的参数证明了这一点。然而，节点名称是一种基准构造，其目的与通过连续空间中的坐标选择点标记相似。图命名（又名同构）被理解为图表上坐标的变化，对应于连续差异的本地分离类似物。我们假定将不变性重命名为对称原理的离散拓扑，其重量与连续的差异不变性相似。我们解释了如何在图形的量子叠加级别上施加重命名不变性，这种方式仍然使我们能够谈论以特定节点为中心的可观察的中心。
We provide a mathematically and conceptually robust notion of quantum superpositions of graphs. We argue that, crucially, quantum superpositions of graphs require node names for their correct alignment, which we demonstrate through a no-signalling argument. Nevertheless, node names are a fiducial construct, serving a similar purpose to the labelling of points through a choice of coordinates in continuous space. Graph renamings, aka isomorphisms, are understood as a change of coordinates on the graph and correspond to a natively discrete analogue of continuous diffeomorphisms. We postulate renaming invariance as a symmetry principle in discrete topology of similar weight to diffeomorphism invariance in the continuous. We explain how to impose renaming invariance at the level of quantum superpositions of graphs, in a way that still allows us to talk about an observable centred at a specific node.
