Entanglement fidelity of Petz decoder for one-shot entanglement transmission

TL;DR

This paper analyzes the entanglement fidelity of the Petz decoder in one-shot quantum entanglement transmission, revealing its dependence on Petz Renyi mutual information and comparing it with other decoders.

Contribution

It demonstrates that the Petz map acts as a universal decoder for one-shot entanglement transmission and links its fidelity to Petz Renyi mutual information.

Findings

Petz map induces a universal decoder for one-shot entanglement transmission.

Entanglement fidelity is determined by Petz Renyi mutual information of order 1/2.

Comparison shows performance differences between Petz, twirled Petz, and Schumacher-Westmoreland decoders.

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.