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In this paper, we extend the resource theory of magic to the channel case byconsidering completely stabilizer preserving operations (CSPOs) as free. Weintroduce and characterize the set of CSPO preserving and completely CSPOpreserving superchannels. We quantify the magic of quantum channels byextending the generalized robustness and the min relative entropy of magic fromthe state to the channel domain and show that they bound the single-shotdynamical magic cost and distillation. We also provide analytical conditionsfor qubit interconversion under CSPOs and show that it is a linear programmingfeasibility problem and hence can be efficiently solved. Lastly, we give aclassical simulation algorithm whose runtime is related to the generalizedrobustness of magic for channels. Our algorithm depends on some pre-definedprecision, and if there is no bound on the desired precision then it achieves aconstant runtime.

Quantifying dynamical magic with completely stabilizer preserving operations as free