Constructing asymmetry monotones from entanglement monotones

We show that any entanglement monotone for bipartite states can be turned into an `asymmetry' monotone, or a quantity that changes monotonically under dynamical time evolutions that preserve the system's phase symmetries. Asymmetry monotones hold information about how a system evolves under symmetry preserving transformations, and are important tools for the detailed study of a system's symmetry properties. Asymmetry monotones also quantify the ability of bounded-size quantum states to substitute for ideal external reference frames and are known as `frameness' monotones in this context. We introduce various new classes of asymmetry monotones both for pure and mixed states and investigate how their properties compare with known bipartite entanglement measures.