Quantification and manipulation of magic channels

In our work, we extend the resource theory of magic from the state domain to the channel domain by introducing and characterizing the set of superchannels that completely preserve the set of completely stabilizer preserving operations. We then extend the generalized robustness of magic and the min relative entropy of magic defined for states to the channel case and show that they bound the single-shot dynamical magic cost and distillation. Lastly, we give a classical simulation algorithm for simulating quantum circuits whose runtime is related to the generalized robustness of magic for channels. Our algorithm depends on some pre-defined precision, and if there is no bound on the desired precision then it achieves a constant runtime.