Symmetry, Asymmetry and quantum information

The asymmetry properties of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for answering the following question: when a system’s dynamics has a particular symmetry, how does this constrain which final states of the system can be reached from a given initial state? This question can be considered for both open-system and closed-system dynamics. It turns out that even for closed-system dynamics, one can find constraints on the possible state evolutions which are stronger than the conservation laws implied by Noether's theorem. Another motivation for the study of asymmetry comes from the field of quantum metrology. It turns out that the degree of success one can achieve in many metrological tasks depends only on the asymmetry properties of the state used for metrology. So a systematic study of these properties can help to develop optimal protocols and strategies for dealing with practical constraints such as noise.