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:1304.3340 · Physical Review A

Detecting quantum non-Gaussianity via the Wigner function

Marco G. Genoni, Mattia L. Palma, Tommaso Tufarelli, Stefano Olivares, M. S. Kim, Matteo G. A. Paris

Published Jun 6, 2013• 109 citations
arXivHTMLPDF

Abstract

We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that cannot be expressed as a convex mixture of Gaussian states. In particular, we prove that for convex mixtures of Gaussian states, the value of the Wigner function at the origin of phase space is bounded from below by a nonzero positive quantity, which is a function only of the average number of excitations (photons) of the state. As a consequence, if this bound is violated, then the quantum state must be quantum non-Gaussian. We show that this criterion can be further generalized by considering additional Gaussian operations on the state under examination. We then apply these criteria to various non-Gaussian states evolving in a noisy Gaussian channel, proving that the bounds are violated for high values of losses, and thus also for states characterized by a positive Wigner function.

DOI
10.1103/physreva.87.062104

Related papers

Quantum non-Gaussianity witnesses in phase space

Catherine Hughes, Marco G. Genoni, Tommaso Tufarelli +2 more

We address detection of quantum non-Gaussian states, i.e., nonclassical states that cannot be expressed as a convex mixture of Gaussian states, and present a method to derive a new family of criteria based on generic linear functionals. We then specialize this method to derive witnesses based on $s$-parametrized quasiprobability functions, generalizing previous criteria based on the Wigner function. In particular, we discuss in detail and analyze the properties of Husimi $Q$-function-based witnesses and prove that they are often more effective than previous criteria in detecting quantum non-Gaussianity of various kinds of non-Gaussian states evolving in a lossy channel.

arXiv:1403.6264•Physical Review A•Jul 10, 2014•64 citations

Detecting Quantum States with a Positive Wigner Function beyond Mixtures of Gaussian States

Radim Filip, Ladislav Mišta

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.

Physical Review Letters•May 16, 2011•134 citations

Sufficient condition for a quantum state to be genuinely quantum non-Gaussian

Lucas Happ, Maxim A. Efremov, Hyunchul Nha +1 more

We show that the expectation value of the operator defined by the position and momentum operators and with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.

New Journal of Physics•Jan 31, 2018•31 citations

Detecting quantum non-Gaussianity of noisy Schrödinger cat states

Mattia L. Palma, Jimmy Stammers, Marco G. Genoni +4 more

Highly quantum nonlinear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schrödinger's cat states, that is, coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schrödinger cat states evolving in a lossy bosonic channel. We prove that the quantum non-Gaussianity can be effectively detected for high values of losses and for large coherent amplitudes of the cat states.

arXiv:1309.4221•Physica Scripta•Apr 1, 2014•6 citations

Testing Nonclassicality and Non-Gaussianity in Phase Space

Jiyong Park, Junhua Zhang, Jaehak Lee +5 more

We theoretically propose and experimentally demonstrate a nonclassicality test of a single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wódkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.

arXiv:1505.01470•Physical Review Letters•May 15, 2015•39 citations

Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state

Jaromír Fiurášek, Lukáš Lachman, Radim Filip

Abstract Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T . We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.

arXiv:2107.09380•New Journal of Physics•Jun 14, 2021•7 citations
We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that cannot be expressed as a convex mixture of Gaussian states. In particular, we prove that for convex mixtures of Gaussian states, the value of the Wigner function at the origin of phase space is bounded from below by a nonzero positive quantity, which is a function only of the average number of excitations (photons) of the state. As a consequence, if this bound is violated, then the quantum state must be quantum non-Gaussian. We show that this criterion can be further generalized by considering additional Gaussian operations on the state under examination. We then apply these criteria to various non-Gaussian states evolving in a noisy Gaussian channel, proving that the bounds are violated for high values of losses, and thus also for states characterized by a positive Wigner function.
We address detection of quantum non-Gaussian states, i.e., nonclassical states that cannot be expressed as a convex mixture of Gaussian states, and present a method to derive a new family of criteria based on generic linear functionals. We then specialize this method to derive witnesses based on sss-parametrized quasiprobability functions, generalizing previous criteria based on the Wigner function. In particular, we discuss in detail and analyze the properties of Husimi QQQ-function-based witnesses and prove that they are often more effective than previous criteria in detecting quantum non-Gaussianity of various kinds of non-Gaussian states evolving in a lossy channel.
We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.
We show that the expectation value of the operator defined by the position and momentum operators and with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.
Highly quantum nonlinear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schrödinger's cat states, that is, coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schrödinger cat states evolving in a lossy bosonic channel. We prove that the quantum non-Gaussianity can be effectively detected for high values of losses and for large coherent amplitudes of the cat states.
We theoretically propose and experimentally demonstrate a nonclassicality test of a single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wódkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.
Abstract Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T . We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.