Revealing nonclassicality beyond Gaussian states via a single marginal distribution

Jiyong Park, Yao Lu, Jaehak Lee, Yangchao Shen, Kuan Zhang, Shuaining Zhang, Muhammad Suhail Zubairy, Kihwan Kim, Hyunchul Nha

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17 Citations (Scopus)


A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential - a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurementaxis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.

Original languageEnglish
Pages (from-to)891-896
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number5
Publication statusPublished - 31 Jan 2017



  • Continuous variable
  • Non-Gaussianity
  • Nonclassicality
  • Quantum entanglement

ASJC Scopus subject areas

  • General

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