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Physical Review A

Quantifying non-Gaussianity of bosonic fields via an uncertainty relation

Shuangshuang Fu, Shunlong Luo, Yue Zhang

Published Jan 30, 2020• 21 citations
Publisher

Abstract

While Gaussian states and associated Gaussian operations are basic ingredients and convenient objects for continuous-variable quantum information, it is also realized that non-Gaussianity is an important resource for quantum information processing. The characterization and quantification of non-Gaussianity have been widely studied in the past decade, with several significant measures for non-Gaussianity introduced. In this work, by exploiting an information-theoretic refinement of the conventional Heisenberg uncertainty relation and a physical characterization of Gaussian states as minimum uncertainty states, we introduce an easily computable measure for non-Gaussianity of bosonic field states in terms of the Wigner-Yanase skew information. Fundamental properties, as well as intuitive meaning, of this measure are unveiled. The concept is illustrated by prototypical non-Gaussian states, and compared with various existent measures for non-Gaussianity. Its merit and physical significance are elucidated.

DOI
10.1103/physreva.101.012125

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While Gaussian states and associated Gaussian operations are basic ingredients and convenient objects for continuous-variable quantum information, it is also realized that non-Gaussianity is an important resource for quantum information processing. The characterization and quantification of non-Gaussianity have been widely studied in the past decade, with several significant measures for non-Gaussianity introduced. In this work, by exploiting an information-theoretic refinement of the conventional Heisenberg uncertainty relation and a physical characterization of Gaussian states as minimum uncertainty states, we introduce an easily computable measure for non-Gaussianity of bosonic field states in terms of the Wigner-Yanase skew information. Fundamental properties, as well as intuitive meaning, of this measure are unveiled. The concept is illustrated by prototypical non-Gaussian states, and compared with various existent measures for non-Gaussianity. Its merit and physical significance are elucidated.
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Abstract Non-Gaussianity is an important resource for quantum information processing with continuous variables. We introduce a measure of the non-Gaussianity of bosonic field states based on the Hellinger distance and present its basic features. This measure has some natural properties and is easy to compute. We illustrate this measure with typical examples of bosonic field states and compare it with various measures of non-Gaussianity. In particular, we highlight its similarity to and difference from the measure based on the Bures distance (or, equivalently, fidelity).
Abstract Two prominent classification schemes for Bosonic field states are (i) classical versus nonclassical, and (ii) Gaussian versus non-Gaussian. These two paradigms are closely related yet fundamentally different. In particular, classical states may be Gaussian or non-Gaussian, and Gaussian states may be classical or nonclassical. Both non-Gaussianity and nonclassicality are important resources for quantum information processing. It is desirable to study the interplay between non-Gaussianity and nonclassicality, and seek effective methods of detecting them. In this work, we introduce a quantifier for non-Gaussianity by exploiting and optimizing an information-theoretic quantifier for nonclassicality, and exhibit its basic properties. A criterion for simultaneously detecting non-Gaussianity and nonclassicality follows, and its applications are illustrated through several examples. This unveils some intrinsic relations between non-Gaussianity and nonclassicality.
We propose a convenient and easily computable nonclassicality quantifier for bosonic field states based on the Wigner-Yanase skew information. The proposed nonclassicality quantifier is reflected by the quantum interaction between the maximum phase angle of the homodyne rotated quadrature operator and the bosonic field states. If the value of the nonclassical quantifier is greater than one-half, the state is nonclassical, and the quantifier is one-half for the pure classical. It is worth mentioning that an increase in the strength of nonclassicality inducing operations, such as squeezing and photon addition, leads to an enhancement of the nonclassicality in the quantum state. By computing some well-known nonclassical states and summarizing their existence features, we have confirmed the validity of our proposed nonclassicality quantifier. We have shown that in a range of values of the nonclassicality of the Gaussian state, revealing the sufficiency of the quantifier. We also compare it with two common nonclassical quantifiers to illustrate its advantages.
Non-Gaussian states are essential resources in quantum information processing. In this work, we investigate methods for quantifying bosonic non-Gaussianity in many-body systems. Building on recent theoretical insights into the self-convolution properties of bosonic pure states, we introduce non-Gaussian entropy as a new measure to characterize non-Gaussianity in bosonic pure states. We further propose a practical protocol for measuring non-Gaussian entropy using three beam splitters and four copies of the input state. In addition, we extend this framework to mixed states, providing a general approach to quantifying non-Gaussianity. Our results offer a convenient and efficient method for characterizing bosonic non-Gaussianity, paving the way for its implementation on near-term experimental platforms.