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

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.

Considerably expanded version with study of Wigner negative volume and of genuine non-Gaussianity of photon-added/subtracted Gaussian states

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• Husimi phase distribution in non-Gaussian operations
• Joint estimation of noise and nonlinearity in Kerr systems
• Almost no experiments have classical Kirkwood-Dirac representations
• Nonclassicality of multi-photon-added cat states
• Isospectral oscillators as a resource for quantum information processing
• Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir