Simulating Symmetric Time Evolutions with Local Operators and Identifying New Selection Rules

For closed systems, time evolution symmetries lead to conservation laws. However, such conservation laws no longer apply to open system that undergo irreversible transformations. Therefore, in such cases, we must look elsewhere for selection rules that help determine what transitions are possible. We show that entanglement theory can address this problem, and that new and more general selection rules can be found solely in terms of entanglement monotones. Our method involves using local operations to simulate a system's symmetric time evolution by first embedding the system's Hilbert space in the tensor product of two Hilbert spaces. Studying how the entanglement of the embedded states change under local operations help us determine what transitions are possible under the initial symmetry. In addition, our results enable us, for the first time, to construct a wide range of new monotones in order to quantify the asymmetric properties of general quantum states. Where the time evolution is reversible, these monotones give rise to totally new conservation laws.