title: Revealing nonclassicality beyond Gaussian states via a single marginal distribution.
abstract: 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 measurement-axis-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.
authors.affiliation: Department of Physics, Texas A&M University at Qatar, Education City, Doha, Qatar.
authors.forename: Jiyong
authors.initials: J
authors.lastname: Park
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Yao
authors.initials: Y
authors.lastname: Lu
authors.affiliation: Department of Physics, Texas A&M University at Qatar, Education City, Doha, Qatar.
authors.forename: Jaehak
authors.initials: J
authors.lastname: Lee
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Yangchao
authors.initials: Y
authors.lastname: Shen
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Kuan
authors.initials: K
authors.lastname: Zhang
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Shuaining
authors.initials: S
authors.lastname: Zhang
authors.affiliation: Department of Physics and Institute of Quantum Studies, Texas A&M University, College Station, TX 77843.
authors.forename: Muhammad Suhail
authors.initials: MS
authors.lastname: Zubairy
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Kihwan
authors.initials: K
authors.lastname: Kim
authors.affiliation: Department of Physics, Texas A&M University at Qatar, Education City, Doha, Qatar; hyunchul.nha@qatar.tamu.edu.
authors.forename: Hyunchul
authors.initials: H
authors.lastname: Nha
keywords: continuous variable; non-Gaussianity; nonclassicality; quantum entanglement