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Neutrino oscillations at the highest energies and longest baselines can be used to study the structure of spacetime and test the fundamental principles of quantum mechanics. If the metric of spacetime has a quantum mechanical description, its fluctuations at the Planck scale are expected to introduce non-unitary effects that are inconsistent with the standard unitary time evolution of quantum mechanics. Neutrinos interacting with such fluctuations would lose their quantum coherence, deviating from the expected oscillatory flavour composition at long distances and high energies. Here we use atmospheric neutrinos detected by the IceCube South Pole Neutrino Observatory in the energy range of 0.5–10.0 TeV to search for coherence loss in neutrino propagation. We find no evidence of anomalous neutrino decoherence and determine limits on neutrino–quantum gravity interactions. The constraint on the effective decoherence strength parameter within an energy-independent decoherence model improves on previous limits by a factor of 30. For decoherence effects scaling as E2 , our limits are advanced by more than six orders of magnitude beyond past measurements compared with the state of the art.