Symmetries of quantum evolutions

Giulio Chiribella, University of Hong Kong

The symmetries of the quantum state space are characterized by Wigner’s celebrated theorem. In this talk, I will discuss the extension of Wigner’s theorem from quantum states to quantum dynamics, characterizing the most general set of symmetries that preserve the set of quantum operations (completely positive, trace non-increasing linear maps). As an application of our general theorem, I will provide a rigorous proof that the set of quantum operations is incompatible with time symmetry in a rather broadly defined sense. Finally, I will discuss a possible time-symmetric variant of quantum theory in which the set of allowed quantum operations is restricted to a proper subset. This variant is compatible with new operations with indefinite time direction, including a new operation called the quantum time flip.

Recording of the talk