Quantum channel simulation has profound physical significance and essentially imitates the behavior of another quantum channel using free operations and resource states, revealing the minimum resources needed to realize a target channel. However, the deterministic channel-simulation process is not always successful. Therefore, it is necessary to study probabilistic channel simulation. In this paper, we study probabilistic channel simulation under the framework of magic (nonstabilizerness) resource theory. First, we give the upper and lower bounds of the maximal success probability of channel simulation under completely stabilizer-preserving operations. Furthermore, as an example, we give the number of copies of different pure magic states needed to simulate the amplitude-damping channel. We also give the semidefinite programming (SDP) to calculate the maximal success probability when the magic states are mixed resource states. Finally, we also study the maximal success probability of channel simulation under completely positive-Wigner-preserving operations and give the corresponding SDP.

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• Quantum channels
• Quantum information processing
• Resource theories