Decoherence and nonclassicality of photon-added/subtracted multi-mode Gaussian states

TL;DR

This paper quantitatively analyzes how photon addition and subtraction increase nonclassicality in multi-mode Gaussian states, highlighting a significant rise in Wigner negativity and QCS, but also increased decoherence susceptibility.

Contribution

It provides explicit formulas for the characteristic and Wigner functions of photon-added/subtracted Gaussian states, enabling quantitative assessment of nonclassicality and quantum non-Gaussianity.

Findings

QCS can increase by up to 200% after photon operations

Photon subtraction certifies quantum non-Gaussianity with positive Wigner function

Photon operations enhance nonclassicality but increase decoherence risk

Abstract

Photon addition and subtraction render Gaussian states non-Gaussian. We provide a quantitative analysis of the change in nonclassicality produced by these processes by analyzing the Wigner negativity and quadrature coherence scale (QCS) of the resulting states. The QCS is a recently introduced measure of nonclassicality [PRL 122, 080402 (2019), PRL 124, 090402 (2020)], that we show to undergo a relative increase under photon addition/subtraction that can be as large as 200\%. This implies that the degaussification and the concomitant increase of nonclassicality come at a cost. Indeed, the QCS is proportional to the decoherence rate of the state so that the resulting states are considerably more prone to environmental decoherence. Our results are quantitative and rely on explicit and general expressions for the characteristic and Wigner functions of photon added/subtracted single- and multi-mode Gaussian states for which we provide a simple and straightforward derivation. These expressions further allow us to certify the quantum non-Gaussianity of the photon-subtracted states with positive Wigner function.