S S symmetry Article Quantum Retrodiction: Foundations and Controversies Stephen M. Barnett 1,* , John Jeffers 2 and David T. Pegg 3 1 School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK 2 Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK;
[email protected] 3 Centre for Quantum Dynamics, School of Science, Griffith University, Nathan 4111, Australia; d.pegg@griffith.edu.au * Correspondence:
[email protected] Abstract: Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on cur- rent information. We present the foundations of quantum retrodiction and highlight its intimate connection with the Bayesian interpretation of probability. The close link with Bayesian methods enables us to explore controversies and misunderstandings about retrodiction that have appeared in the literature. To be clear, quantum retrodiction is universally applicable and draws its validity directly from conventional predictive quantum theory coupled with Bayes’ theorem. Keywords: quantum foundations; bayesian inference; time reversal 1. Introduction Quantum theory is usually presented as a predictive theory, with statements made concerning the probabilities for measurement outcomes based upon earlier preparation events. In retrodictive quantum theory this order is reversed and we seek to use the Citation: Barnett, S.M.; Jeffers, J.; outcome of a measurement to make probabilistic statements concerning earlier events [1–6]. Pegg, D.T. Quantum Retrodiction: The theory was first presented within the context of time-reversal symmetry [1–3] but, more Foundations and Controversies. recently, has been developed into a practical tool for analysing experiments in quantum Symmetry 2021, 13, 586.