Journal
NATURE PHYSICS
Volume 11, Issue 10, Pages 853-U176Publisher
NATURE PORTFOLIO
DOI: 10.1038/NPHYS3414
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Funding
- European Commission under the Marie Curie Intra-European Fellowship Programme [PIEF-GA-2010-273119]
- F.R.S.-FNRS under the Charge de recherches (CR) Fellowship Programme
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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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