Symmetries of quantum evolutions

Understand

A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigner's theorem.

• Wigner's theorem establishes that every symmetry of the quantum state space must be either a unitary transformation, or an antiunitary transformation.
• Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated to the dynamics of closed systems, and the stochastic evolutions associated to the outcomes of quantum measurements.
• We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary.