Heralded processes on continuous-variable spaces as quantum maps

TL;DR

This paper introduces a new way to represent heralded quantum processes in continuous-variable systems using transfer functions on Wigner functions, enabling better analysis of experimental imperfections.

Contribution

It proposes a novel transfer function framework for quantum maps in continuous variables and reconstructs key processes like noiseless amplification and photon addition from experimental data.

Findings

Transfer function representation accurately models heralded processes.

Reconstruction of noiseless amplification and photon addition maps.

Analysis of experimental imperfections' impact on quantum processes.

Abstract

Conditional evolution is crucial for generating non-Gaussian resources for quantum information tasks in the continuous variable scenario. However, tools are lacking for a convenient representation of heralded process in terms of quantum maps for continuous variable states, in the same way as Wigner functions are able to give a compact description of the quantum state. Here we propose and study such a representation, based on the introduction of a suitable transfer function to describe the action of a quantum operation on the Wigner function. We also reconstruct the maps of two relevant examples of conditional process, that is, noiseless amplification and photon addition, by combining experimental data and a detailed physical model. This analysis allows to fully characterize the effect of experimental imperfections in their implementations.