Quantum Channel Simulation under Purified Distance is no more difficult than State Splitting

Characterizing the minimal communication needed for the quantum channel simulation is a fundamental task in the quantum information theory. In this paper, we show that, under the purified distance, the quantum channel simulation can be directly achieved via quantum state splitting without using a technique known as the de Finetti reduction, and thus provide a pair of tighter one-shot bounds. Using the bounds, we also recover the quantum reverse Shannon theorem in a much simpler way.