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Certification of Non-Gaussian States with Operational Measurements

Ulysse Chabaud1,2,*, Ganaël Roeland3, Mattia Walschaers3, Frédéric Grosshans2, Valentina Parigi3, Damian Markham2,4, and Nicolas Treps3

  • 1Université de Paris, IRIF, CNRS, Paris, France
  • 2Sorbonne Université, LIP6, CNRS, 4 place Jussieu, Paris 75005, France
  • 3Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, Paris F-75252, France
  • 4JFLI, CNRS, National Institute of Informatics, University of Tokyo, Tokyo, Japan

  • *ulysse.chabaud@gmail.com
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PRX Quantum 2, 020333 – Published 3 June, 2021Erratum PRX Quantum 6, 010902 (2025)

DOI: https://doi.org/10.1103/PRXQuantum.2.020333

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.

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Erratum

Erratum: Certification of non-Gaussian States with Operational Measurements [PRX Quantum 2, 020333 (2021)]

Ulysse Chabaud, Ganaël Roeland, Mattia Walschaers, Frédéric Grosshans, Valentina Parigi, Damian Markham, and Nicolas Treps
PRX Quantum 6, 010902 (2025)

Popular Summary

Quantum technologies are predicted to offer dramatic advantages over existing technologies for computing, communication, and cryptography. However, there is still a long way to go before this theorized revolution becomes a reality. Indeed, quantum information is fragile and can easily be lost when the physical system that carries it interacts with its environment. The development of quantum technologies is therefore difficult and greatly depends on the existence of efficient tools to assess the relevant properties of quantum systems. In particular, the so-called non-Gaussian properties are essential features for any quantum computational advantage using quantum states of light, but they have remained challenging to detect and characterize in complex quantum systems. In this work, we resolve this challenge and provide efficient methods for the experimental investigation of non-Gaussian properties of quantum states.

By studying the robustness of non-Gaussian properties of quantum states, we deduce how to compute robust benchmarks for these properties from simple experimental measurements of the states. Importantly, our results show that the certification of non-Gaussian features can actually be carried out efficiently experimentally with current technology and is not prohibited by an unreachable amount of required samples. We demonstrate the applicability of our methods with numerical and experimental data for both single-mode and multimode systems.

Our findings pave the way for the development of light-based quantum technologies, with direct applications in existing quantum-optics experiments. Our work also motivates future studies of fundamental problems such as the intriguing link between two key quantum properties: non-Gaussianity and entanglement.

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Outline

Information

PRX Quantum 2, 020333– Published 3 June, 2021
  • Received 9 November 2020
  • Revised 30 April 2021
  • Accepted 5 May 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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