Entanglement fidelity of Petz decoder for one-shot entanglement transmission

Abstract: 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 Renyi mutual information of order 1/2 associated with a complementary channel, thus providing an 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.