Symmetries of quantum evolutions

A cornerstone of quantum mechanics is the characterization symmetries provided by Wigner's theorem. theorem establishes that every symmetry state space must be either a unitary transformation or an antiunitary transformation. Here we extend from states to evolutions, including both deterministic evolution associated with dynamics closed systems and stochastic evolutions outcomes measurements. We prove can decomposed into two are antiunitary. Building on this result, show it impossible time-reversal full set evolutions. Our no-go implies any time-symmetric formulation theory restrict allowed modify operational interpretation processes. propose where restricted suitable set, which includes projective measurements but excludes preparation pure states. The standard retrieved version introducing operation conditioning past experiments.