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arXiv · 1507.07745

Operational formulation of time reversal in quantum theory

Ognyan Oreshkov·Nicolas J. Cerf
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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 via 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 those assumed before. This suggests a possible direction for search of extensions of known physics.

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Ognyan Oreshkov, Nicolas J. Cerf. 2016-07-29. Operational formulation of time reversal in quantum theory. https://doi.org/10.1038/nphys3414

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