Entanglement fidelity of the Petz decoder for one-shot entanglement transmission

One-shot entanglement transmission is a quantum information processing task where a quantum state is sent to a second party over a noisy channel. The goal of the task is to approximately recover the original state by applying a decoder to the output of the noisy channel. In this work, we note that the Petz map induces a universal decoder for one-shot entanglement transmission, and we quantify its entanglement fidelity. This fidelity is found to be determined by the singly minimized Petz Rényi mutual information of order 1/2 associated with a complementary channel, thus providing a novel operational interpretation of this information measure. Furthermore, we compare the performance of this decoder to that of the decoder induced by the twirled Petz map and the Schumacher–Westmoreland decoder.