- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Verifying energy-time entanglement with irregularly sampled correlations

James Schneeloch1,*, Christopher C. Tison1,†, Richard J. Birrittella2, Ian Brinkley3,4, Michael L. Fanto1,5, and Paul M. Alsing1

  • *Contact author: james.schneeloch.1@afrl.af.mil
  • †Contact author: christopher.tison.2@afrl.af.mil
PDF

Phys. Rev. Research 7, 033096 – Published 28 July, 2025

DOI: https://doi.org/10.1103/6nws-mlgs

Abstract

Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the energy-time degree of freedom, this challenge is exacerbated because realistic high-resolution frequency measurements are obtained as a function of light passing through arbitrary filters positioned at uneven intervals. In this work, we show how the data gathered from these kinds of measurements can be used to fully certify the degree of energy and timing correlations needed to certify energy-time entanglement without having to make special assumptions about the state or the measurement device. We accomplish this by showing how to construct a continuous-variable probability density from the data that can closely estimate, but never overestimate the correlations (and entanglement) actually present in the system, and note that these methods are applicable to all continuous-variable degrees of freedom (e.g., spatial, field quadratures, etc.). We illustrate the feasibility of these methods using frequency and timing correlations obtainable from photon pairs in spontaneous parametric down-conversion.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (26)

  1. J. Schneeloch, C. C. Tison, M. L. Fanto, P. M. Alsing, and G. A. Howland, Quantifying entanglement in a 68-billion-dimensional quantum state space, Nat. Commun. 10, 2785 (2019).
  2. Y. Mei, Y. Zhou, S. Zhang, J. Li, K. Liao, H. Yan, S.-L. Zhu, and S. Du, Einstein-Podolsky-Rosen energy-time entanglement of narrow-band biphotons, Phys. Rev. Lett. 124, 010509 (2020).
  3. J. Schneeloch and G. A. Howland, Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations, Phys. Rev. A 97, 042338 (2018).
  4. L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, Three-photon energy–time entanglement, Nat. Phys. 9, 19 (2013).
  5. M. Liscidini and J. E. Sipe, Stimulated emission tomography, Phys. Rev. Lett. 111, 193602 (2013).
  6. J.-P. W. MacLean, J. M. Donohue, and K. J. Resch, Direct characterization of ultrafast energy-time entangled photon pairs, Phys. Rev. Lett. 120, 053601 (2018).
  7. S. P. Walborn, B. G. Taketani, A. Salles, F. Toscano, and R. L. de Matos Filho, Entropic entanglement criteria for continuous variables, Phys. Rev. Lett. 103, 160505 (2009).
  8. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley and Sons, New York, NY, 2006).
  9. S. P. Walborn, A. Salles, R. M. Gomes, F. Toscano, and P. H. S. Ribeiro, Revealing hidden Einstein-Podolsky-Rosen nonlocality, Phys. Rev. Lett. 106, 130402 (2011).
  10. I. Białynicki-Birula and J. Mycielski, Uncertainty relations for information entropy in wave mechanics, Commun. Math. Phys. 44, 129 (1975).
  11. H. M. Wiseman, S. J. Jones, and A. C. Doherty, Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox, Phys. Rev. Lett. 98, 140402 (2007).
  12. A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935).
  13. J. Schneeloch, P. B. Dixon, G. A. Howland, C. J. Broadbent, and J. C. Howell, Violation of continuous-variable Einstein-Podolsky-Rosen steering with discrete measurements, Phys. Rev. Lett. 110, 130407 (2013).
  14. J. Schneeloch, S. H. Knarr, G. A. Howland, and J. C. Howell, Demonstrating continuous variable Einstein–Podolsky–Rosen steering in spite of finite experimental capabilities using Fano steering bounds, J. Opt. Soc. Am. B 32, A8 (2015).
  15. F. Toscano, D. S. Tasca, L. Rudnicki, and S. P. Walborn, Uncertainty relations for coarse–grained measurements: An overview, Entropy 20, 454 (2018).
  16. J. Schneeloch, C. C. Tison, H. S. Jacinto, and P. M. Alsing, Negativity vs. purity and entropy in witnessing entanglement, Sci. Rep. 13, 4601 (2023).
  17. A. Marshall, I. Olkin, and B. Arnold, Inequalities: Theory of Majorization and Its Applications, Springer Series in Statistics (Springer, New York, NY, 2010).
  18. M. A. Nielsen and J. Kempe, Separable states are more disordered globally than locally, Phys. Rev. Lett. 86, 5184 (2001).
  19. J. Schneeloch and J. C. Howell, Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone, J. Opt. 18, 053501 (2016).
  20. K. Kato and E. Takaoka, Sellmeier and thermo-optic dispersion formulas for KTP, Appl. Opt. 41, 5040 (2002).
  21. B. P. Ramsay, O. T. Koppius, and E. L. Cleveland, The prism and the theory of optical resolution, J. Opt. Soc. Am. 30, 439 (1940).
  22. D. J. Starling, S. M. Bloch, P. K. Vudyasetu, J. S. Choi, B. Little, and J. C. Howell, Double Lorentzian atomic prism, Phys. Rev. A 86, 023826 (2012).
  23. M. Shirasaki, Virtually imaged phased array as a wavelength demultiplexer (U.S. Patent 5 999 320, Dec. 7, 1999), https://patents.justia.com/patent/5999320#history.
  24. S. Xiao, A. M. Weiner, and C. Lin, A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory, IEEE J. Quantum Electron. 40, 420 (2004).
  25. S. Xiao and A. M. Weiner, 2-D wavelength demultiplexer with potential for ≥1000 channels in the C-band, Opt. Express 12, 2895 (2004).
  26. X. Zhu, D. Lin, Z. Hao, L. Wang, and J. He, A VIPA spectrograph with ultra-high resolution and wavelength calibration for astronomical applications, Astron. J. 160, 135 (2020).

Outline

Information

Phys. Rev. Research 7, 033096– Published 28 July, 2025
  • Received 9 December 2024
  • Accepted 11 July 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation