Detecting non-Gaussianity via nonclassicality

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.

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

“…Our result is consistent with Ref. [37], in which the non-Gaussianity of even/odd Schrödinger cat states can be detected by the information-theoretic quantifier for non-classicality.…”

“…We can see that the intrinsic relation between non-classicality and non-Gaussianity of quantum states were established by the information-theoretic means. [37] In addition, an entanglement criterion with the third-and fourth-order cumulants was used to detect the entanglement of non-Gaussian states. [41] Therefore, in the future work we will try to link the higher-order cumulants or cumulant matrix of the state analyzed with its quantum correlations, thereby formulating a methodology for characterizing quantum correlations in terms of cumulant theory.…”

Generation of nonclassical states by superposition of number-conserving operations on squeezed thermal state

“…The nonclassicality of quantum states has been an interesting topic of quantum information processing in recent years [1][2][3][4][5][6][7][8]. In particular, it has been proven that the nonclassicality is closely associated with the phase sensitivity [5,[9][10][11].…”