Document Open Access Logo

Building Trust for Continuous Variable Quantum States

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



PDF
Thumbnail PDF

File

LIPIcs.TQC.2020.3.pdf
  • Filesize: 0.61 MB
  • 15 pages

Document Identifiers

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

Acknowledgements

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)
https://doi.org/10.4230/LIPIcs.TQC.2020.3

Abstract

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
Keywords
  • Continuous variable quantum information
  • reliable state tomography
  • certification
  • verification

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Leandro Aolita, Christian Gogolin, Martin Kliesch, and Jens Eisert. Reliable quantum certification of photonic state preparations. Nature communications, 6:8498, 2015. URL: https://doi.org/10.1038/ncomms9498.
  2. Stephen D. Bartlett, Barry C. Sanders, Samuel L. Braunstein, and Kae Nemoto. Efficient classical simulation of continuous variable quantum information processes. Phys. Rev. Lett., 88:097904, February 2002. URL: https://doi.org/10.1103/PhysRevLett.88.097904.
  3. C. H. Bennett and G. Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proc. IEEE International Conference on Computers, Systems and Signal Processing, volume 175, page 8, Bangalore, December 1984. URL: https://doi.org/10.1016/j.tcs.2011.08.039.
  4. Samuel L. Braunstein and Peter van Loock. Quantum information with continuous variables. Rev. Mod. Phys., 77:513-577, June 2005. URL: https://doi.org/10.1103/RevModPhys.77.513.
  5. Kevin E Cahill and Roy J Glauber. Density operators and quasiprobability distributions. Physical Review, 177(5):1882, 1969. URL: https://doi.org/10.1103/PhysRev.177.1882.
  6. Ulysse Chabaud, Tom Douce, Frédéric Grosshans, Elham Kashefi, and Damian Markham. Building trust for continuous variable quantum states. CoRR, 2019. URL: http://arxiv.org/abs/1905.12700.
  7. Matthias Christandl and Renato Renner. Reliable quantum state tomography. Physical Review Letters, 109(12):120403, 2012. URL: https://doi.org/10.1103/PhysRevLett.109.120403.
  8. G. M. D'Ariano and H. P. Yuen. Impossibility of measuring the wave function of a single quantum system. Physical review letters, 76(16):2832, 1996. URL: https://doi.org/10.1103/PhysRevLett.76.2832.
  9. G Mauro D'Ariano, Matteo GA Paris, and Massimiliano F Sacchi. Quantum tomography. Advances in Imaging and Electron Physics, 128:206-309, 2003. URL: http://arxiv.org/abs/quant-ph/0302028.
  10. Jens Eisert, Stefan Scheel, and Martin B Plenio. Distilling gaussian states with gaussian operations is impossible. Physical review letters, 89(13):137903, 2002. URL: https://doi.org/10.1103/PhysRevLett.89.137903.
  11. Alessandro Ferraro, Stefano Olivares, and Matteo GA Paris. Gaussian states in continuous variable quantum information. CoRR, 2005. URL: http://arxiv.org/abs/quant-ph/0503237.
  12. Jaromír Fiurášek. Gaussian transformations and distillation of entangled gaussian states. Physical review letters, 89(13):137904, 2002. URL: https://doi.org/10.1103/PhysRevLett.89.137904.
  13. Christopher A Fuchs and Jeroen Van De Graaf. Cryptographic distinguishability measures for quantum-mechanical states. IEEE Transactions on Information Theory, 45(4):1216-1227, 1999. Google Scholar
  14. Alexandru Gheorghiu, Theodoros Kapourniotis, and Elham Kashefi. Verification of quantum computation: An overview of existing approaches. Theory of Computing Systems, 4:715-808, 2019. URL: https://doi.org/10.1007/s00224-018-9872-3.
  15. Wassily Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American statistical association, 58(301):13-30, 1963. URL: https://doi.org/10.1080/01621459.1963.10500830.
  16. Anthony Leverrier, Raúl García-Patrón, Renato Renner, and Nicolas J Cerf. Security of continuous-variable quantum key distribution against general attacks. Physical review letters, 110(3):030502, 2013. URL: https://doi.org/10.1103/PhysRevLett.110.030502.
  17. Nana Liu, Tommaso F Demarie, Si-Hui Tan, Leandro Aolita, and Joseph F Fitzsimons. Client-friendly continuous-variable blind and verifiable quantum computing. Physical Review A, 100(6):062309, 2019. URL: https://doi.org/PhysRevA.100.062309.
  18. Seth Lloyd and Samuel L Braunstein. Quantum computation over continuous variables. In Quantum Information with Continuous Variables, pages 9-17. Springer, 1999. URL: https://doi.org/10.1103/PhysRevLett.82.1784.
  19. Alexander I Lvovsky and Michael G Raymer. Continuous-variable optical quantum-state tomography. Reviews of Modern Physics, 81(1):299, 2009. URL: https://doi.org/10.1103/RevModPhys.81.299.
  20. Julien Niset, Jaromír Fiurášek, and Nicolas J Cerf. No-go theorem for gaussian quantum error correction. Physical review letters, 102(12):120501, 2009. URL: https://doi.org/10.1103/PhysRevLett.102.120501.
  21. Matteo GA Paris. On density matrix reconstruction from measured distributions. Optics communications, 124(3-4):277-282, 1996. URL: https://doi.org/10.1016/0030-4018(96)00019-3.
  22. Matteo GA Paris. Quantum state measurement by realistic heterodyne detection. Physical Review A, 53(4):2658, 1996. URL: https://doi.org/10.1103/PhysRevA.53.2658.
  23. John Preskill. Quantum computing in the nisq era and beyond. Quantum, 2:79, 2018. URL: https://doi.org/10.22331/q-2018-08-06-79.
  24. Renato Renner and J Ignacio Cirac. de finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography. Physical review letters, 102(11):110504, 2009. URL: https://doi.org/10.1103/PhysRevLett.102.110504.
  25. Yuki Takeuchi, Atul Mantri, Tomoyuki Morimae, Akihiro Mizutani, and Joseph F Fitzsimons. Resource-efficient verification of quantum computing using serfling’s bound. npj Quantum Information, 5:27, 2019. URL: https://doi.org/10.1038/s41534-019-0142-2.
  26. Yong Siah Teo, Christian R Muller, Hyunseok Jeong, Zdenek Hradil, Jaroslav Rehacek, and Luis L Sanchez-Soto. When heterodyning beats homodyning: an assessment with quadrature moments. CoRR, 2017. URL: http://arxiv.org/abs/1701.07539.
  27. Thomas Vidick. http://users.cms.caltech.edu/~vidick/verification_bulletin.pdf, 2018. URL: http://users.cms.caltech.edu/~vidick/verification_bulletin.pdf.
  28. Eugene Paul Wigner. On the quantum correction for thermodynamic equilibrium. In Part I: Physical Chemistry. Part II: Solid State Physics, pages 110-120. Springer, 1997. URL: https://doi.org/10.1103/PhysRev.40.749.
  29. Alfred Wünsche. Laguerre 2d-functions and their application in quantum optics. Journal of Physics A: Mathematical and General, 31(40):8267, 1998. URL: https://doi.org/10.1088/0305-4470/31/40/017.
  30. Shota Yokoyama, Ryuji Ukai, Seiji C Armstrong, Chanond Sornphiphatphong, Toshiyuki Kaji, Shigenari Suzuki, Jun-ichi Yoshikawa, Hidehiro Yonezawa, Nicolas C Menicucci, and Akira Furusawa. Ultra-large-scale continuous-variable cluster states multiplexed in the time domain. Nature Photonics, 7(12):982, 2013. URL: https://doi.org/10.1038/nphoton.2013.287.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail