Linking asymmetry of quantum states to entanglement

Quantum evolutions that preserve a certain symmetry are expressed as covariant transformations. We show how covariant transformations can be simulated by local operations by embedding the system's Hilbert space in the tensor product of two Hilbert spaces. The embedding maps symmetric states to separable bipartite states in the larger Hilbert space and some asymmetric states to entangled states. We show how entanglement of the bipartite image state can be used to quantify the asymmetry of the original state. Our results make it possible for the first time to construct a wide range of asymmetry monotones for general symmetry groups associated with different superselection rules, and highlights the deep links that exist between entanglement theory and the resource theories of asymmetry.