On quantum superpositions of graphs, no-signalling and covariance

• URL: http://arxiv.org/abs/2010.13579v3
• Date: Tue, 7 Mar 2023 23:14:35 GMT
• Title: On quantum superpositions of graphs, no-signalling and covariance
• Authors: Pablo Arrighi and Marios Christodoulou and Am\'elia Durbec
• Abstract summary: 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. We explain how to impose renaming invariance at the level of quantum superpositions of graphs.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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