Giulio Chiribella, University of Hong Kong

The symmetries of the quantum state space are characterized by Wignerâ€™s celebrated theorem. In this talk, I will discuss the extension of Wignerâ€™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