Abstract
The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born’s rule do not apply backward in time. Here, we resolve this problem within a rigorous operational probabilistic framework. We argue that reconciling time reversal with the probabilistic rules of the theory requires a notion of operation that permits realizations through both pre- and post-selection. We develop the generalized formulation of quantum theory that stems from this approach and give a precise definition of time-reversal symmetry, emphasizing a previously overlooked distinction between states and effects. We prove an analogue of Wigner’s theorem, which characterizes all allowed symmetry transformations in this operationally time-symmetric quantum theory. Remarkably, we find larger classes of symmetry transformations than previously assumed, suggesting a possible direction in the search for extensions of known physics.
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Acknowledgements
This work was supported by the European Commission under the Marie Curie Intra-European Fellowship Programme (PIEF-GA-2010-273119) and by the F.R.S.–FNRS under the Chargé de recherches (CR) Fellowship Programme.
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O.O. conceived the project, developed the concepts and wrote the manuscript. N.J.C. supervised the project, discussed the results and edited the manuscript.
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Oreshkov, O., Cerf, N. Operational formulation of time reversal in quantum theory. Nature Phys 11, 853–858 (2015). https://doi.org/10.1038/nphys3414
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DOI: https://doi.org/10.1038/nphys3414
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