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 novel insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1-dim marginal distribution into a factorized 2-dim 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 an 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, i.e. detection of genuine non-Gaussianity under a CV measurement.

6 pages, 4 figures with Supplemental Information

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• Efficient construction of witnesses of stellar rank of nonclassical states of light
• Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state
• Quantum non-Gaussianity certification of photon-number-resolving detectors
• Certification of stellar ranks of quantum states of light with a pair of click detectors
• Non-Gaussian entanglement criteria for atomic homodyne detection
• Quantum entanglement and extractable work for Gaussian states
• Quantum signatures and semiclassical limitations in the transmission of Fock states
• Optimal noisy quantum phase estimation with finite-dimensional states