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arXiv:2011.04320 · PRX Quantum

Certification of Non-Gaussian States with Operational Measurements

Ulysse Chabaud, Ganaël Roeland, Mattia Walschaers, Frédéric Grosshans, Valentina Parigi, Damian Markham, Nicolas Treps

Published Jun 3, 2021• 60 citations
arXivHTMLPDF

Abstract

We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection.We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses.We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity.Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states.Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous-variable quantum states, and show that certification of high-order non-Gaussian features can be carried out experimentally with current technology.

DOI
10.1103/prxquantum.2.020333

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We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection.We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses.We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity.Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states.Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous-variable quantum states, and show that certification of high-order non-Gaussian features can be carried out experimentally with current technology.
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Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of certifying application-specific quantities using measurements that are not tomographically complete, i.e. that provide only partial information about the state related to the application of interest. Here, we focus on simplifying the measurements needed to certify non-Gaussianity in bosonic systems, a resource related to quantum advantage in various information processing tasks. We show that the statistics of a single quadrature measurement, corresponding to standard homodyne detection in quantum optics, can witness arbitrary degrees of non-Gaussianity as quantified by stellar rank. Our results are based on a version of Hudson's theorem for wavefunctions, proved in a companion paper [arXiv:2507.23468], revealing that the zeros in a homodyne distribution are signatures of quantum non-Gaussianity and higher stellar ranks. The validity of our witnesses is supported by a technical result showing that sets of states with bounded energy and finite stellar rank are compact. We provide an analysis of sample complexity, noise robustness, and experimental prospects. Our work drastically simplifies the setup required to detect quantum non-Gaussianity in bosonic quantum states.
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Quantum correlations are at the core of current developments in quantum technologies.Certification protocols of entanglement and steering, suitable for continuous-variable non-Gaussian states are scarce and generally highly demanding from an experimental point of view.We propose a protocol based on Fisher information for witnessing steering in general continuous-variable bipartite states, through homodyne detection.It proves to be relevant for the detection of non-Gaussian steering in scenarios where witnesses based on Gaussian features like the covariance matrix are shown to fail.