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  • Featured in Physics
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Quick Quantum Steering: Overcoming Loss and Noise with Qudits

Vatshal Srivastav1,*, Natalia Herrera Valencia1, Will McCutcheon1, Saroch Leedumrongwatthanakun1, Sébastien Designolle2, Roope Uola2, Nicolas Brunner2, and Mehul Malik1,†

  • 1Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
  • 2Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland

  • *vs54@hw.ac.uk
  • †m.malik@hw.ac.uk
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Phys. Rev. X 12, 041023 – Published 30 November, 2022

DOI: https://doi.org/10.1103/PhysRevX.12.041023

Abstract

A primary requirement for a robust and unconditionally secure quantum network is the establishment of quantum nonlocal correlations over a realistic channel. While loophole-free tests of Bell nonlocality allow for entanglement certification in such a device-independent setting, they are extremely sensitive to loss and noise, which naturally arise in any practical communication scenario. Quantum steering relaxes the strict technological constraints of Bell nonlocality by reframing it in an asymmetric manner, with a trusted party only on one side. However, tests of quantum steering still require either extremely high-quality entanglement or very low loss. Here we introduce a test of quantum steering that harnesses the advantages of high-dimensional entanglement to be simultaneously noise robust and loss tolerant. Despite being constructed for qudits, our steering test is designed for single-detector measurements and is able to close the fair-sampling loophole in a time-efficient manner. We showcase the improvements over qubit-based systems by experimentally demonstrating quantum steering in up to 53 dimensions, free of the fair-sampling loophole, through simultaneous loss and noise conditions corresponding to 14.2-dB loss equivalent to 79 km of telecommunication fiber, and 36% of white noise. We go on to show how the use of high dimensions counterintuitively leads to a dramatic reduction in total measurement time, enabling a quantum steering violation almost 2 orders of magnitude faster obtained by simply doubling the Hilbert space dimension. Our work conclusively demonstrates the significant resource advantages that high-dimensional entanglement provides for quantum steering in terms of loss, noise, and measurement time, and opens the door toward practical quantum networks with the ultimate form of security.

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synopsis

Quantum Steering That’s Robust to Loss and Noise

Published 30 November, 2022

Researchers demonstrate a loss-tolerant method for so-called quantum steering, a phenomenon that could give quantum communication networks complete security.

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Popular Summary

Quantum entanglement enables the most secure form of communication possible—one where the communication devices themselves can be in the hands of an adversary, and security is still guaranteed. However, distributing entanglement over long distances and through a noisy environment is not easy. Entangled photons can be lost while propagating through fibers, and detectors can be compromised by large amounts of noise. As a result, tests of quantum nonlocality—the most stringent form of entanglement—have been performed only under very controlled conditions. Quantum steering relaxes the strict requirements of nonlocality by assuming an untrusted device only on one side of an untrusted channel. In our work, we harness the advantages of high-dimensional entanglement to demonstrate quantum steering with the detection loophole closed under extreme conditions of noise and loss.

We develop a new test of quantum steering that requires only a single detector at each end, regardless of the dimension of the entanglement used. Using this test, we “steer” entanglement through loss equivalent to that encountered in 79 km of telecom fiber amidst white noise that makes up 36 percent of the signal probability. Remarkably, our technique also leads to a dramatic reduction in the total measurement time needed: By simply doubling the entanglement dimensionality, we reduce the measurement time by almost 2 orders of magnitude.

Our work demonstrates that the fundamental phenomenon of entanglement can indeed transcend the limits imposed by a realistic environment and opens a clear pathway toward quantum communication protocols with unconditional security.

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References (68)

  1. Nicolas Gisin and Rob Thew, Quantum Communication, Nat. Photonics, 1, 165 (2007).
  2. Eleni Diamanti, Hoi-Kwong Lo, Bing Qi, and Zhiliang Yuan, Practical Challenges in Quantum Key Distribution, npj Quantum Inf. 2, 16025 (2016).
  3. Mario Krenn, Mehul Malik, Thomas Scheidl, Rupert Ursin, and Anton Zeilinger, Quantum Communication with Photons (Springer International Publishing, Cham, 2016), pp. 455–482.
  4. Feihu Xu, Xiongfeng Ma, Qiang Zhang, Hoi-Kwong Lo, and Jian-Wei Pan, Secure Quantum Key Distribution with Realistic Devices, Rev. Mod. Phys. 92, 025002 (2020).
  5. Valerio Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, N. Lutkenhaus, and M. Peev, The Security of Practical Quantum Key Distribution, Rev. Mod. Phys. 81, 1301 (2009).
  6. Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani, Device-Independent Security of Quantum Cryptography against Collective Attacks, Phys. Rev. Lett. 98, 230501 (2007).
  7. Marissa Giustina et al., Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons, Phys. Rev. Lett. 115, 250401 (2015).
  8. Lynden K. Shalm et al., Strong Loophole-Free Test of Local Realism, Phys. Rev. Lett. 115, 250402 (2015).
  9. B. Hensen et al., Loophole-Free Bell Inequality Violation Using Electron Spins Separated by 1.3 Kilometres, Nature (London) 526, 682 (2015).
  10. Philip M. Pearle, Hidden-Variable Example Based upon Data Rejection, Phys. Rev. D 2, 1418 (1970).
  11. N. Gisin and B. Gisin, A Local Hidden Variable Model of Quantum Correlation Exploiting the Detection Loophole, Phys. Lett. A 260, 323 (1999).
  12. 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).
  13. Daniel Cavalcanti and Paul Skrzypczyk, Quantum Steering: A Review with Focus on Semidefinite Programming, Rep. Prog. Phys. 80, 024001 (2017).
  14. Roope Uola, Ana C. S. Costa, H. Chau Nguyen, and Otfried Gühne, Quantum Steering, Rev. Mod. Phys. 92, 015001 (2020).
  15. E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid, Experimental Criteria for Steering and the Einstein-Podolsky-Rosen Paradox, Phys. Rev. A 80, 032112 (2009).
  16. D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde, Experimental EPR-Steering Using Bell-Local States, Nat. Phys. 6, 845 (2010).
  17. Bernhard Wittmann, Sven Ramelow, Fabian Steinlechner, Nathan K Langford, Nicolas Brunner, Howard M Wiseman, Rupert Ursin, and Anton Zeilinger, Loophole-Free Einstein-Podolsky-Rosen Experiment via Quantum Steering, New J. Phys. 14, 053030 (2012).
  18. A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, Arbitrarily Loss-Tolerant Einstein-Podolsky-Rosen Steering Allowing a Demonstration over 1 km of Optical Fiber with No Detection Loophole, Phys. Rev. X 2, 031003 (2012).
  19. Devin H. Smith et al., Conclusive Quantum Steering with Superconducting Transition-Edge Sensors, Nat. Commun. 3, 625 (2012).
  20. Morgan M. Weston, Sergei Slussarenko, Helen M. Chrzanowski, Sabine Wollmann, Lynden K. Shalm, Varun B. Verma, Michael S. Allman, Sae Woo Nam, and Geoff J. Pryde, Heralded Quantum Steering over a High-Loss Channel, Sci. Adv. 4, e1701230 (2018).
  21. Daniele Cozzolino, Beatrice Da Lio, Davide Bacco, and Leif Katsuo Oxenløwe, High-Dimensional Quantum Communication: Benefits, Progress, and Future Challenges, Adv. Quantum Technol. 2, 1900038 (2019).
  22. Manuel Erhard, Mario Krenn, and Anton Zeilinger, Advances in High Dimensional Quantum Entanglement, Nat. Rev. Phys. 2, 365 (2020).
  23. Nicolas Brunner, S. Pironio, A. Acin, N. Gisin, A. A. Methot, and V. Scarani, Testing the Dimension of Hilbert Spaces, Phys. Rev. Lett. 100, 210503 (2008).
  24. Sébastien Designolle, Robust Genuine High-Dimensional Steering with Many Measurements, Phys. Rev. A 105, 032430 (2022).
  25. Tamás Vertesi, Stefano Pironio, and Nicolas Brunner, Closing the Detection Loophole in Bell Experiments Using Qudits, Phys. Rev. Lett. 104, 060401 (2010).
  26. H. Bechmann-Pasquinucci and W. Tittel, Quantum Cryptography Using Larger Alphabets, Phys. Rev. A 61, 062308 (2000).
  27. Nicolas J. Cerf, Mohamed Bourennane, Anders Karlsson, and Nicolas Gisin, Security of Quantum Key Distribution Using d-Level Systems, Phys. Rev. Lett. 88, 127902 (2002).
  28. Mehul Malik and Robert W Boyd, Quantum Imaging Technologies, Nuovo Cimento 37, 273 (2014).
  29. Lana Sheridan and Valerio Scarani, Security Proof for Quantum Key Distribution Using Qudit Systems, Phys. Rev. A 82, 030301(R) (2010).
  30. J. Nunn, L. J. Wright, C. Söller, L. Zhang, I. A. Walmsley, and B. J. Smith, Large-Alphabet Time-Frequency Entangled Quantum Key Distribution by Means of Time-to-Frequency Conversion, Opt. Express 21, 15959 (2013).
  31. Zheshen Zhang, Jacob Mower, Dirk Englund, Franco N. C. Wong, and Jeffrey H. Shapiro, Unconditional Security of Time-Energy Entanglement Quantum Key Distribution Using Dual-Basis Interferometry, Phys. Rev. Lett. 112, 120506 (2014).
  32. Mohammad Mirhosseini, Omar S Magaña-Loaiza, Malcolm N O’Sullivan, Brandon Rodenburg, Mehul Malik, Martin P J Lavery, Miles J Padgett, Daniel J Gauthier, and Robert W Boyd, High-Dimensional Quantum Cryptography with Twisted Light, New J. Phys. 17, 033033 (2015).
  33. Matej Pivoluska, Marcus Huber, and Mehul Malik, Layered Quantum Key Distribution, Phys. Rev. A 97, 032312 (2018).
  34. Sebastian Ecker et al., Overcoming Noise in Entanglement Distribution, Phys. Rev. X 9, 041042 (2019).
  35. F. Zhu, M. Tyler, N. H. Valencia, M. Malik, and J. Leach, Is High-Dimensional Photonic Entanglement Robust to Noise?, AVS Quantum Sci. 3, 011401 (2021).
  36. Natalia Herrera Valencia, Suraj Goel, Will McCutcheon, Hugo Defienne, and Mehul Malik, Unscrambling Entanglement through a Complex Medium, Nat. Phys. 16, 1112 (2020).
  37. Huan Cao et al., Distribution of High-Dimensional Orbital Angular Momentum Entanglement over a 1 km Few-Mode Fiber, Optica 7, 232 (2020).
  38. Manuel Erhard, Mehul Malik, and Anton Zeilinger, A Quantum Router for High-Dimensional Entanglement, Quantum Sci. Technol. 2, 014001 (2017).
  39. Fabian Steinlechner, Sebastian Ecker, Matthias Fink, Bo Liu, Jessica Bavaresco, Marcus Huber, Thomas Scheidl, and Rupert Ursin, Distribution of High-Dimensional Entanglement via an Intra-City Free-Space Link, Nat. Commun. 8, 15971 (2017).
  40. Mhlambululi Mafu, Angela Dudley, Sandeep Goyal, Daniel Giovannini, Melanie McLaren, Miles J. Padgett, Thomas Konrad, Francesco Petruccione, Norbert Lütkenhaus, and Andrew Forbes, Higher-Dimensional Orbital-Angular-Momentum-Based Quantum Key Distribution with Mutually Unbiased Bases, Phys. Rev. A 88, 032305 (2013).
  41. Sébastien Designolle, V. Srivastav, R. Uola, N. H. Valencia, W. McCutcheon, M. Malik, and N. Brunner, Genuine High-Dimensional Quantum Steering, Phys. Rev. Lett. 126, 200404 (2021).
  42. Rui Qu, Y. Wang, M. An, F. Wang, Q. Quan, H. Li, H. Gao, F. Li, and P. Zhang, Retrieving High-Dimensional Quantum Steering from a Noisy Environment with N Measurement Settings, Phys. Rev. Lett. 128, 240402 (2022).
  43. Marcus Huber and Marcin Pawłowski, Weak Randomness in Device-Independent Quantum Key Distribution and the Advantage of Using High-Dimensional Entanglement, Phys. Rev. A 88, 032309 (2013).
  44. Takuya Ikuta and Hiroki Takesue, Implementation of Quantum State Tomography for Time-Bin Qudits, New J. Phys. 19, 013039 (2017).
  45. Nicolas K. Fontaine, Roland Ryf, Haoshuo Chen, David T. Neilson, Kwangwoong Kim, and Joel Carpenter, Laguerre-Gaussian Mode Sorter, Nat. Commun. 10, 1865 (2019).
  46. Suraj Goel et al., Inverse-Design of High-Dimensional Quantum Optical Circuits in a Complex Medium, arXiv:2204.00578.
  47. William K. Wootters and Brian D. Fields, Optimal State-Determination by Mutually Unbiased Measurements, Ann. Phys. (N.Y.) 191, 363 (1989).
  48. Ana Belén Sainz, Yelena Guryanova, Will McCutcheon, and Paul Skrzypczyk, Adjusting Inequalities for Detection-Loophole-Free Steering Experiments, Phys. Rev. A 94, 032122 (2016).

  49. This assumes a fiber loss of 0.18 to 0.2  dB/km, as provided by ultralow-loss telecom fiber.

  50. Frédéric Bouchard, Natalia Herrera Valencia, Florian Brandt, Robert Fickler, Marcus Huber, and Mehul Malik, Measuring Azimuthal and Radial Modes of Photons, Opt. Express 26, 31925 (2018).
  51. Hammam Qassim, Filippo M. Miatto, Juan P. Torres, Miles J. Padgett, Ebrahim Karimi, and Robert W. Boyd, Limitations to the Determination of a Laguerre-Gauss Spectrum via Projective, Phase-Flattening Measurement, J. Opt. Soc. Am. B 31, A20 (2014).
  52. Serge Massar and Stefano Pironio, Violation of Local Realism versus Detection Efficiency, Phys. Rev. A 68, 062109 (2003).
  53. Reinhard F. Werner, Quantum States with Einstein-Podolsky-Rosen Correlations Admitting a Hidden-Variable Model, Phys. Rev. A 40, 4277 (1989).
  54. Vatshal Srivastav, Natalia Herrera Valencia, Saroch Leedumrongwatthanakun, Will McCutcheon, and Mehul Malik, Characterising and Tailoring Spatial Correlations in Multimode Parametric Down-Conversion, Phys. Rev. Appl. 18, 054006 (2022).
  55. Natalia Herrera Valencia, Vatshal Srivastav, Matej Pivoluska, Marcus Huber, Nicolai Friis, Will McCutcheon, and Mehul Malik, High-Dimensional Pixel Entanglement: Efficient Generation and Certification, Quantum 4, 376 (2020).
  56. Victor Arrizón, Ulises Ruiz, Rosibel Carrada, and Luis A. González, Pixelated Phase Computer Holograms for the Accurate Encoding of Scalar Complex Fields, J. Opt. Soc. Am. A 24, 3500 (2007).
  57. Mohammad Mirhosseini, Omar S. Magaña-Loaiza, Changchen Chen, Brandon Rodenburg, Mehul Malik, and Robert W. Boyd, Rapid Generation of Light Beams Carrying Orbital Angular Momentum, Opt. Express 21, 30196 (2013).
  58. Michael Kues, Christian Reimer, Joseph M. Lukens, William J. Munro, Andrew M. Weiner, David J. Moss, and Roberto Morandotti, Quantum Optical Microcombs, Nat. Photonics 13, 170 (2019).
  59. Daniel Llewellyn et al., Chip-to-Chip Quantum Teleportation and Multi-Photon Entanglement in Silicon, Nat. Phys. 16, 148 (2020).
  60. Bo Jing et al., Entanglement of Three Quantum Memories via Interference of Three Single Photons, Nat. Photonics 13, 210 (2019).
  61. M. Pompili et al., Realization of a Multinode Quantum Network of Remote Solid-State Qubits, Science 372, 259 (2021).
  62. Antonio Acín, Daniel Cavalcanti, Elsa Passaro, Stefano Pironio, and Paul Skrzypczyk, Necessary Detection Efficiencies for Secure Quantum Key Distribution and Bound Randomness, Phys. Rev. A 93, 012319 (2016).
  63. Cyril Branciard, Eric G. Cavalcanti, Stephen P. Walborn, Valerio Scarani, and Howard M. Wiseman, One-Sided Device-Independent Quantum Key Distribution: Security, Feasibility, and the Connection with Steering, Phys. Rev. A 85, 010301(R) (2012).
  64. Joseph F. Fitzsimons, Private Quantum Computation: An Introduction to Blind Quantum Computing and Related Protocols, npj Quantum Inf. 3, 23 (2017).
  65. Fuad Kittaneh, Norm Inequalities for Certain Operator Sums, J. Funct. Anal. 143, 337 (1997).
  66. Marco Tomamichel, Serge Fehr, Jędrzej Kaniewski, and Stephanie Wehner, A Monogamy-of-Entanglement Game with Applications to Device-Independent Quantum Cryptography, New J. Phys. 15, 103002 (2013).
  67. Paul Skrzypczyk and Daniel Cavalcanti, Loss-Tolerant Einstein-Podolsky-Rosen Steering for Arbitrary-Dimensional States: Joint Measurability and Unbounded Violations under Losses, Phys. Rev. A 92, 022354 (2015).
  68. Paul Skrzypczyk and Daniel Cavalcanti, Maximal Randomness Generation from Steering Inequality Violations Using Qudits, Phys. Rev. Lett. 120, 260401 (2018).

Outline

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Phys. Rev. X 12, 041023– Published 30 November, 2022
  • Received 26 April 2022
  • Revised 29 September 2022
  • Accepted 21 October 2022
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