Preparation of arbitrary quantum states with regular $P$~functions

TL;DR

This paper introduces a quantum optical device that regularizes the highly singular Glauber-Sudarshan $P$ functions of quantum states, enabling the creation of nonclassical states with regular $P$ functions for improved quantum measurements.

Contribution

The authors propose a novel experimental setup for regularizing $P$ functions of quantum states, facilitating direct sampling without additional regularization or reconstruction.

Findings

Numerical simulations confirm the feasibility of the proposed method.

The approach allows direct sampling of output states with regular $P$ functions.

Generalization to multimode light is outlined.

Abstract

We propose a quantum optical device to experimentally realize quantum processes, which perform the regularization of the---in general highly singular---Glauber-Sudarshan $P$~functions of arbitrary quantum states before their application and/or measurement. This allows us to produce a broad class of nonclassical states with regular $P$~functions, also called nonclassicality quasiprobabilities. For this purpose, the input states are combined on highly transmissive beam splitters with specific Gaussian or non-Gaussian classical states. We study both balanced and unbalanced homodyne detections for the direct sampling of the output states of the implemented processes, which requires no further regularization or state-reconstruction. By numerical simulations we demonstrate the feasibility of our approach and we outline the generalization to multimode light.