Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1905.06755 · Physical Review A

Mode-dependent-loss model for multimode photon-subtracted states

Mattia Walschaers, Young-Sik Ra, Nicolas Treps

Published Aug 19, 2019• 15 citations
arXivHTMLPDF

Abstract

Multimode photon subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the payoff for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equations to describe losses in $n$-photon-subtracted multimode states, where each photon can be subtracted in an arbitrary mode. As a main result, we find that mode-dependent losses and photon subtraction generally do not commute. In particular, the losses do not only reduce the purity of the state, they also change the modal structure of its non-Gaussian features. We then conduct a detailed study of single-photon subtraction from a multimode Gaussian state, which is a setting that lies within the reach of present-day experiments.

DOI
10.1103/physreva.100.023828

Related papers

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

Mattia Walschaers, Claude Fabre, Valentina Parigi +1 more

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

arXiv:1707.02285•Physical Review Letters•Oct 31, 2017•94 citations

Decoherence and nonclassicality of photon-added and photon-subtracted multimode Gaussian states

Anaelle Hertz, Stephan De Bièvre

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 [Phys. Rev. Lett. 122, 080402 (2019); Phys. Rev. Lett. 124, 090402 (2020)], which we show to undergo a relative increase under photon addition and 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 and -subtracted single- and multimode 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.

Physical Review A•Apr 26, 2023•17 citations

General Photon Subtraction from a Gaussian Perspective

Niklas Budinger, Ulrik L. Andersen, Peter van Loock

A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.

quant-pharXiv:2609.34803•Sep 29, 2026•0 citations

Multimode model for projective photon-counting measurements

Rosa Tualle-Brouri, Alexei Ourjoumtsev, Aurélien Dantan +3 more

We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-Gaussian states are produced conditionally. These are useful states for continuous-variable quantum-information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric down-conversion, thereby improving the analysis of existing experimental results. The main improvement is that spatial and frequency filters before the photon detector are taken into account explicitly. We find excellent agreement with previously published experimental results, using fewer free parameters than before, and discuss the implications of our analysis for the optimized production of states with negative Wigner functions.

Physical Review A•Jul 9, 2009•25 citations

Statistical signatures of multimode single-photon-added and -subtracted states of light

Mattia Walschaers, Claude Fabre, Valentina Parigi +1 more

The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this paper we derive the truncated correlations, which are multimode generalizations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.

arXiv:1708.08412•Physical Review A•Nov 14, 2017•44 citations

A multimode framework to describe photon subtraction operation

Mohamed Faouzi Melalkia, F. Brunel, Sébastien Tanzilli +2 more

Optical non-Gaussian quantum states can be generated in a heralded manner by applying a photon subtraction operation to a Gaussian input state. In our work, we develop a theoretical framework to describe this operation in the case where the input state is spectrally multimode. This framework allows the optimal design of photon subtraction experiments. We give the exact expression of the generated non-Gaussian state in the general case. We apply this framework to the case of Schrodinger kitten state generation using a multimode squeezed vacuum as input state. We show that the quality of the generated state (in terms of fidelity and Wigner function negativity) can be enhanced by adapting the different experimental parameters.

•Oct 10, 2021•0 citations
Multimode photon subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the payoff for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equations to describe losses in nnn-photon-subtracted multimode states, where each photon can be subtracted in an arbitrary mode. As a main result, we find that mode-dependent losses and photon subtraction generally do not commute. In particular, the losses do not only reduce the purity of the state, they also change the modal structure of its non-Gaussian features. We then conduct a detailed study of single-photon subtraction from a multimode Gaussian state, which is a setting that lies within the reach of present-day experiments.
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
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 [Phys. Rev. Lett. 122, 080402 (2019); Phys. Rev. Lett. 124, 090402 (2020)], which we show to undergo a relative increase under photon addition and 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 and -subtracted single- and multimode 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.
A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.
We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-Gaussian states are produced conditionally. These are useful states for continuous-variable quantum-information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric down-conversion, thereby improving the analysis of existing experimental results. The main improvement is that spatial and frequency filters before the photon detector are taken into account explicitly. We find excellent agreement with previously published experimental results, using fewer free parameters than before, and discuss the implications of our analysis for the optimized production of states with negative Wigner functions.
The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this paper we derive the truncated correlations, which are multimode generalizations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.
Optical non-Gaussian quantum states can be generated in a heralded manner by applying a photon subtraction operation to a Gaussian input state. In our work, we develop a theoretical framework to describe this operation in the case where the input state is spectrally multimode. This framework allows the optimal design of photon subtraction experiments. We give the exact expression of the generated non-Gaussian state in the general case. We apply this framework to the case of Schrodinger kitten state generation using a multimode squeezed vacuum as input state. We show that the quality of the generated state (in terms of fidelity and Wigner function negativity) can be enhanced by adapting the different experimental parameters.