Operational formulation of time reversal in quantum theory

• Published in: Nature physics Vol. 11; no. 10; pp. 853 - 858
• Main Authors: Oreshkov, Ognyan, Cerf, Nicolas J.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.10.2015; Nature Publishing Group
• Subjects: 639/766/483/1139; 639/766/483/481; 639/766/483/640; Atomic; Classical and Continuum Physics; Complex Systems; Condensed Matter Physics; Formulations; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Physics; Probabilistic methods; Probability theory; Quantum physics; Quantum theory; Searching; Stems; Symmetry; Theoretical; Transformations
• ISSN: 1745-2473; 1745-2481
• DOI: 10.1038/nphys3414

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. A reformulation of quantum theory aims at reconciling transition probabilities with time reversal in connection to Wigner’s notion of symmetry, expanding the known classes of symmetry transformations.