On quantum superpositions of graphs, no-signalling and covariance
Year: 2025
Type: article
Abstract: We provide a mathematically and conceptually robust notion of quantum superpositions of graphs. The formalism may be useful for the purpose of modelling a ‘fully quantum internet’ and states of geometry in quantum gravity. We argue that quantum superpositions of graphs do require node names for their correct alignment, which we demonstrate through a no-signalling argument. The need for node names was often overlooked or disagreed upon in previous proposals. Still, node names should remain 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. We explain how to impose renaming invariance at the level of operators over quantum superpositions of graphs, in a way that still allows us to talk about local operators.
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Paris-Saclay, Laboratoire Méthodes Formelles, University of Vienna, Austrian Academy of Sciences, Vienna Center for Quantum Science and Technology, Laboratoire Interdisciplinaire des Sciences du Numérique
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4409097161