© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1803.03133 · Physical Review A

Quantum non-Gaussianity and quantification of nonclassicality

B. Kühn, W. Vogel

Published May 17, 2018• 32 citations

Abstract

The algebraic quantification of nonclassicality, which naturally arises from the quantum superposition principle, is related to properties of regular nonclassicality quasiprobabilities. The latter are obtained by non-Gaussian filtering of the Glauber-Sudarshan $P$ function. They yield lower bounds for the degree of nonclassicality. We also derive bounds for convex combinations of Gaussian states for certifying quantum non-Gaussianity directly from the experimentally accessible nonclassicality quasiprobabilities. Other quantum-state representations, such as $s$-parametrized quasiprobabilities, insufficiently indicate or even fail to directly uncover detailed information on the properties of quantum states. As an example, our approach is applied to multi-photon-added squeezed vacuum states.

DOI: 10.1103/physreva.97.053823

Related papers

Quantifying nonclassicality by characteristic functions

S. Ryl, Jan Sperling, W. Vogel

In this paper, we use the characteristic function, i.e., the Fourier transform of the Glauber-Sudarshan phase-space distribution, to determine the degree of nonclassicality of a given state. This degree of nonclassicality quantifies the nonclassicality in terms of quantum superpositions. We demonstrate two ways to exactly find or to lower-bound the degree of nonclassicality by studying the properties of the characteristic functions. The developed criteria are applied to two examples of squeezed states undergoing a classical mixing or a nonclassical superposition with vacuum.

arXiv:1702.00213•Physical Review A•May 9, 2017•30 citations

Nonclassicality filters and quasiprobabilities

T. Kiesel, W. Vogel

Necessary and sufficient conditions for the nonclassicality of bosonic quantum states are formulated by introducing nonclassicality filters and nonclassicality quasiprobability distributions. Regular quasiprobabilities are constructed from characteristic functions which can be directly sampled by balanced homodyne detection. Their negativities uncover the nonclassical effects of general quantum states. The method is illustrated by visualizing the nonclassical nature of a squeezed state.

arXiv:1004.0788•Physical Review A•Sep 13, 2010•75 citations

Nonclassicality, entanglement, and nonclassical correlations

W. Vogel, Jan Sperling

Nonclassicality of quantum states is characterized by a regularized Glauber-Sudarshan P-function. Related characterizations of entanglement are derived from so-called separability eigenvalue equations. General quantum correlations and the quantification of quantum phenomena are studied.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2013•0 citations

Visualizing nonclassical effects in phase space

B. Kühn, W. Vogel

Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan $P$ function, also denoted as nonclassicality quasiprobability. Such filters are introduced and analyzed for optimizing the experimental certification of nonclassical effects. An analytic filter is constructed which preserves the full information on the quantum state. For balanced homodyne detection, the number of data points is analyzed to get the negativities of the nonclassicality quasiprobability with high statistical significance. The method is applied to different scenarios, such as phase-randomized squeezed vacuum states, single-photon-added thermal states, and heralded state engineering with array detectors. The generalization to visualize quantum correlations of multimode radiation fields is also considered.

arXiv:1407.5768•Physical Review A•Sep 15, 2014•17 citations

Nonclassicality criteria: Quasiprobability distributions and correlation functions

Moorad Alexanian

We use the exact calculation of the quantum mechanical, temporal characteristic function $\ensuremath{\chi}(\ensuremath{\eta})$ and the degree of second-order coherence ${g}^{(2)}(\ensuremath{\tau})$ for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state, to study the different criteria for nonclassicality. In particular, we contrast criteria that involve only one-time functions of the dynamical system, for instance, the quasiprobability distribution $P(\ensuremath{\beta})$ of the Glauber-Sudarshan coherent or P representation of the density of state and the Mandel ${Q}_{M}(\ensuremath{\tau})$ parameter, versus the criteria associated with the two-time correlation function ${g}^{(2)}(\ensuremath{\tau})$.

arXiv:1610.08829•Physical Review A•Oct 20, 2016•5 citations

Experimental determination of a nonclassical Glauber-Sudarshan P function

T. Kiesel, W. Vogel, Valentina Parigi +2 more

A quantum state is nonclassical if its Glauber-Sudarshan $P$ function fails to be interpreted as a probability density. This quantity is often highly singular, so that its reconstruction is a demanding task. Here we present the experimental determination of a well-behaved $P$ function showing negativities for a single-photon-added thermal state. This is a direct visualization of the original definition of nonclassicality. The method can be useful under conditions for which many other signatures of nonclassicality would not persist.

arXiv:0804.1016•Physical Review A•Aug 25, 2008•102 citations

The algebraic quantification of nonclassicality, which naturally arises from the quantum superposition principle, is related to properties of regular nonclassicality quasiprobabilities. The latter are obtained by non-Gaussian filtering of the Glauber-Sudarshan

P

function. They yield lower bounds for the degree of nonclassicality. We also derive bounds for convex combinations of Gaussian states for certifying quantum non-Gaussianity directly from the experimentally accessible nonclassicality quasiprobabilities. Other quantum-state representations, such as

s

-parametrized quasiprobabilities, insufficiently indicate or even fail to directly uncover detailed information on the properties of quantum states. As an example, our approach is applied to multi-photon-added squeezed vacuum states.

In this paper, we use the characteristic function, i.e., the Fourier transform of the Glauber-Sudarshan phase-space distribution, to determine the degree of nonclassicality of a given state. This degree of nonclassicality quantifies the nonclassicality in terms of quantum superpositions. We demonstrate two ways to exactly find or to lower-bound the degree of nonclassicality by studying the properties of the characteristic functions. The developed criteria are applied to two examples of squeezed states undergoing a classical mixing or a nonclassical superposition with vacuum.

Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan

P

function, also denoted as nonclassicality quasiprobability. Such filters are introduced and analyzed for optimizing the experimental certification of nonclassical effects. An analytic filter is constructed which preserves the full information on the quantum state. For balanced homodyne detection, the number of data points is analyzed to get the negativities of the nonclassicality quasiprobability with high statistical significance. The method is applied to different scenarios, such as phase-randomized squeezed vacuum states, single-photon-added thermal states, and heralded state engineering with array detectors. The generalization to visualize quantum correlations of multimode radiation fields is also considered.

We use the exact calculation of the quantum mechanical, temporal characteristic function $\ensuremath{\chi}(\ensuremath{\eta})$ and the degree of second-order coherence ${g}^{(2)}(\ensuremath{\tau})$ for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state, to study the different criteria for nonclassicality. In particular, we contrast criteria that involve only one-time functions of the dynamical system, for instance, the quasiprobability distribution $P(\ensuremath{\beta})$ of the Glauber-Sudarshan coherent or P representation of the density of state and the Mandel ${Q}_{M}(\ensuremath{\tau})$ parameter, versus the criteria associated with the two-time correlation function ${g}^{(2)}(\ensuremath{\tau})$.

A quantum state is nonclassical if its Glauber-Sudarshan

P

function fails to be interpreted as a probability density. This quantity is often highly singular, so that its reconstruction is a demanding task. Here we present the experimental determination of a well-behaved

P

function showing negativities for a single-photon-added thermal state. This is a direct visualization of the original definition of nonclassicality. The method can be useful under conditions for which many other signatures of nonclassicality would not persist.