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Signatures of causality and determinism in a quantum theory of events

Aditya Iyer1,*, Eduardo O. Dias2,†, and Vlatko Vedral1,3,4,‡

  • 1Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
  • 2Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil
  • 3Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 117543
  • 4Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542

  • *aditya.iyer@physics.ox.ac.uk
  • †eduardo.dias@ufpe.br
  • ‡vlatko.vedral@physics.ox.ac.uk

Phys. Rev. A 105, L010202 – Published 14 January, 2022

DOI: https://doi.org/10.1103/PhysRevA.105.L010202

Abstract

By representing an event as the joint state of a detector-timer couple that interacts with a system, we recover the familiar tensor product structure, used to describe spatially separated systems, in the context of timelike events. Furthermore, with this approach, we extend the superposition principle to the moment of occurrence of events. We then outline quantum signatures of causality that manifest through coherence in the detector state and correlation functions of time operators. Finally, we expand the scope of quantum information theoretic measures of state discrimination and information content, commonly used to characterize spatially separated systems, to events in spacetime. For causally connected events, we illustrate a deterministic relationship between events (akin to spatially entangled physical systems) where observing a previous event (one subsystem) enables us to delineate a later event (the other subsystem).

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