Recovery of optical losses with the Petz recovery map

TL;DR

This paper explores the use of the Petz recovery map to improve the correction of optical losses in quantum systems, demonstrating its near-optimal performance over other protocols.

Contribution

It constructs and analyzes the Petz recovery map for single-mode optical losses, showing its advantages and limitations in quantum information recovery.

Findings

Petz recovery map outperforms belief state replacement in recovery performance.

When the reference state is far from the true state, it's better not to apply Petz recovery.

Petz recovery is near-optimal among considered protocols.

Abstract

Optical systems are a main platform for quantum information processing, while a hidden challenge in these systems is information loss due to scattering into unmonitored modes, typically modeled as state-independent beam-splitter interactions. While such losses simply erase information encoded across modes, they directly degrade information encoded in the quantum state of a mode. Perfect correction of these Gaussian lossy channels with Gaussian operations alone is known to be impossible. In this work, we investigate the Petz recovery map as an approximate recovery. We construct the Petz recovery of single mode losses and its implementations. In particular, we show that the recovery performance of Petz recovery map is better than the recovery protocol that replaces the noisy state with the belief state. Also, when the reference state is far from the true state, it is better not to use the Petz recovery map but to leave the noisy state instead. We discuss the physical intuition of Petz recovery map and finally shows that it is near-optimal among the considered recovery protocols.