Quantifying Multiqubit Magic Channels with Completely Stabilizer-Preserving Operations

In this paper we extend the resource theory of magic states to the channel domain by considering completely stabilizer-preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO-preserving and completely CSPO-preserving superchannels. We quantify magic channels by extending the generalized robustness and the min-relative entropy defined for magic states to channels and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear programming feasibility problem and hence can be efficiently solved. Lastly, we give a classical simulation algorithm whose runtime is related to the generalized robustness of magic channels. Our algorithm depends on some predefined precision, and if there is no bound on the desired precision then it achieves a constant runtime.