Building Trust for Continuous Variable Quantum States

Authors Ulysse Chabaud , Tom Douce, Frédéric Grosshans , Elham Kashefi, Damian Markham

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Author Details

Ulysse Chabaud
  • Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
Tom Douce
  • School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom
Frédéric Grosshans
  • Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
  • Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405 Orsay Cedex, France
Elham Kashefi
  • Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
  • School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom
Damian Markham
  • Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France


We thank N. Treps, V. Parigi, and especially M. Walschaers for stimulating discussions. We also thank A. Leverrier for interesting discussion on de Finetti reductions, and useful comments on previous versions of this work. This work was supported by the ANR project ANR-13-BS04-0014 COMB.

Cite AsGet BibTex

Ulysse Chabaud, Tom Douce, Frédéric Grosshans, Elham Kashefi, and Damian Markham. Building Trust for Continuous Variable Quantum States. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In this work we develop new methods for the characterisation of continuous variable quantum states using heterodyne measurement in both the trusted and untrusted settings. First, building on quantum state tomography with heterodyne detection, we introduce a reliable method for continuous variable quantum state certification, which directly yields the elements of the density matrix of the state considered with analytical confidence intervals. This method neither needs mathematical reconstruction of the data nor discrete binning of the sample space and uses a single Gaussian measurement setting. Second, beyond quantum state tomography and without its identical copies assumption, we promote our reliable tomography method to a general efficient protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries, i.e., making no assumptions whatsoever on the state generated by the adversary. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over the Fock basis, computed with samples from heterodyne detection of the state.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum information theory
  • Continuous variable quantum information
  • reliable state tomography
  • certification
  • verification


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