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

Entropy

Estimating Non-Gaussianity of a Quantum State by Measuring Orthogonal Quadratures

Jiyong Park

Published Feb 18, 2022• 3 citations
Publisher

Abstract

We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.

DOI
10.3390/e24020289

Related papers

Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions

Jiyong Park, Jaehak Lee, Kyunghyun Baek +1 more

We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian unitary operations, and monotonicity under Gaussian channels. Furthermore, we find a quantitative relation between our measure and the previously proposed non-Gaussianity measures defined via quantum relative entropy and the quantum Hilbert-Schmidt distance. This allows us to estimate the non-Gaussianity measures readily by homodyne detection, which would otherwise require a full quantum-state tomography.

arXiv:2109.14353•Physical Review A•Sep 17, 2021•17 citations

Quantifying non-Gaussianity for quantum information

Marco G. Genoni, Matteo G. A. Paris

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

arXiv:1008.4243•Physical Review A•Nov 30, 2010•201 citations

Entropic nonclassicality and quantum non-Gaussianity tests via beam splitting

Jiyong Park, Jaehak Lee, Hyunchul Nha

We propose entropic nonclassicality criteria for quantum states of light that can be readily tested using homodyne detection with beam splitting operation. Our method draws on the fact that the entropy of quadrature distributions for a classical state is non-increasing under an arbitrary loss channel. We show that our test is strictly stronger than the variance-based squeezing condition and that it can also be extended to detect quantum non-Gaussianity in conjunction with phase randomization. Furthermore, we address how our criteria can be used to identify single-mode resource states to generate two-mode states demonstrating EPR paradox, i.e., quantum steering, via beam-splitter setting.

Scientific Reports•Nov 28, 2019•10 citations

Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states

Kyunghyun Baek, Hyunchul Nha

We suggest an improved version of the Robertson--Schr\"odinger uncertainty relation for canonically conjugate variables by taking into account a pair of characteristics of states: non-Gaussianity and mixedness quantified by using fidelity and entropy, respectively. This relation is saturated by both Gaussian and Fock states and provides a strictly improved bound for any non-Gaussian states or mixed states. For the case of Gaussian states, it is reduced to the entropy-bounded uncertainty relation derived by Dodonov. Furthermore, we consider readily computable measures of both characteristics and find a weaker but more readily accessible bound. With its generalization to the case of two-mode states, we show applicability of the relation to detect entanglement of non-Gaussian states.

arXiv:1811.10207•Physical Review A•Oct 10, 2018•14 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

Nonclassicality and entanglement for continuous-variable quantum information

Hyunchul Nha, Jaehak Lee, Jiyong Park

We present how nonclassicality and entanglement can be characterized and detected efficiently for continuous variable systems. Of particular interest is the use of homodyne detections to measure quadrature amplitudes at minimum level to confirm nonclassicality and entanglement beyond Gaussian states. We introduce a systematic method for a functional form of uncertainty relations, which can be efficiently employed to experimentally detect non-Gaussian states comprehensively. Our approach for quantum correlations unifies a framework for quantum entanglement and quantum steering, which include the known results for Gaussian states and provides a better tool for non-Gaussian states than existing methods, e.g. entropic uncertainty relations.

SPIE Conference on Quantum and Nonlinear Optics•Nov 9, 2018•0 citations
We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.
We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian unitary operations, and monotonicity under Gaussian channels. Furthermore, we find a quantitative relation between our measure and the previously proposed non-Gaussianity measures defined via quantum relative entropy and the quantum Hilbert-Schmidt distance. This allows us to estimate the non-Gaussianity measures readily by homodyne detection, which would otherwise require a full quantum-state tomography.
We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.
We propose entropic nonclassicality criteria for quantum states of light that can be readily tested using homodyne detection with beam splitting operation. Our method draws on the fact that the entropy of quadrature distributions for a classical state is non-increasing under an arbitrary loss channel. We show that our test is strictly stronger than the variance-based squeezing condition and that it can also be extended to detect quantum non-Gaussianity in conjunction with phase randomization. Furthermore, we address how our criteria can be used to identify single-mode resource states to generate two-mode states demonstrating EPR paradox, i.e., quantum steering, via beam-splitter setting.
We suggest an improved version of the Robertson--Schr\"odinger uncertainty relation for canonically conjugate variables by taking into account a pair of characteristics of states: non-Gaussianity and mixedness quantified by using fidelity and entropy, respectively. This relation is saturated by both Gaussian and Fock states and provides a strictly improved bound for any non-Gaussian states or mixed states. For the case of Gaussian states, it is reduced to the entropy-bounded uncertainty relation derived by Dodonov. Furthermore, we consider readily computable measures of both characteristics and find a weaker but more readily accessible bound. With its generalization to the case of two-mode states, we show applicability of the relation to detect entanglement of non-Gaussian states.
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.
We present how nonclassicality and entanglement can be characterized and detected efficiently for continuous variable systems. Of particular interest is the use of homodyne detections to measure quadrature amplitudes at minimum level to confirm nonclassicality and entanglement beyond Gaussian states. We introduce a systematic method for a functional form of uncertainty relations, which can be efficiently employed to experimentally detect non-Gaussian states comprehensively. Our approach for quantum correlations unifies a framework for quantum entanglement and quantum steering, which include the known results for Gaussian states and provides a better tool for non-Gaussian states than existing methods, e.g. entropic uncertainty relations.