Room 117

Operational formulation of time reversal in quantum theory

C. Jebarathinam

IMSc

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.

Journal reference: Nature Physics 11, 853–858 (2015) doi:10.1038/nphys3414