- 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
  • Letter
  • Open Access

Optimal squeezing for quantum target detection

Gaetana Spedalieri and Stefano Pirandola

  • Department of Computer Science, University of York, York YO10 5GH, United Kingdom

PDF

Phys. Rev. Research 3, L042039 – Published 10 December, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042039

Abstract

It is not clear if the performance of a quantum lidar or radar, without an idler and only using Gaussian resources, could exceed the performance of a semiclassical setup based on coherent states and homodyne detection. Here we prove this is indeed the case by showing that an idler-free squeezed-based setup can beat this semiclassical benchmark. More generally, we show that probes whose displacement and squeezing are jointly optimized can strictly outperform coherent states with the same mean number of input photons for both the problems of quantum illumination and reading.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. C. W. Helstrom, Quantum Detection and Estimation Theory, Mathematics in Science and Engineering, Vol. 123 (Academic, New York, 1976).
  2. A. Chefles, Quantum state discrimination, Contemp. Phys. 41, 401 (2000).
  3. U. Herzog and J. A. Bergou, Optimum unambiguous discrimination of two mixed quantum states, Phys. Rev. A 71, 050301(R) (2005).
  4. S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photonics 1, 238 (2009).
  5. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
  6. S. Pirandola, B. Roy Bardhan, T. Gehring, C. Weedbrook, and S. Lloyd, Advances in photonic quantum sensing, Nat. Photonics 12, 724 (2018).
  7. S. Lloyd, Enhanced sensitivity of photodetection via quantum illumination, Science 321, 1463 (2008).
  8. S. H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, Quantum Illumination with Gaussian States, Phys. Rev. Lett. 101, 253601 (2008).
  9. E. D. Lopaeva, I. Ruo Berchera, I. P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, Experimental Realization of Quantum Illumination, Phys. Rev. Lett. 110, 153603 (2013).
  10. Z. Zhang, M. Tengner, T. Zhong, F. N. C. Wong, and J. H. Shapiro, Entanglement's Benefit Survives an Entanglement-Breaking Channel, Phys. Rev. Lett. 111, 010501 (2013).
  11. S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, Microwave Quantum Illumination, Phys. Rev. Lett. 114, 080503 (2015).
  12. Q. Zhuang, Z. Zhang, and J. H. Shapiro, Entanglement enhanced Neyman–Pearson target detection using quantum illumination, J. Opt. Soc Am. B 34, 1567 (2017).
  13. G. De Palma and J. Borregaard, Minimum error probability of quantum illumination, Phys. Rev. A 98, 012101 (2018).
  14. C. W. Sandbo Chang, A. M. Vadiraj, J. Bourassa, B. Balaji, and C. M. Wilson, Quantum-enhanced noise radar, Appl. Phys. Lett. 114, 112601 (2019).
  15. S. Barzanjeh, S. Pirandola, D. Vitali, and J. M. Fink, Experimental microwave quantum illumination, Sci. Adv. 6, eabb0451 (2020).
  16. R. Nair and M. Gu, Fundamental limits of quantum illumination, Optica 7, 771 (2020).
  17. A. Karsa, G. Spedalieri, Q. Zhuang, and S. Pirandola, Quantum Illumination with a generic Gaussian source, Phys. Rev. Research 2, 023414 (2020).
  18. S.-Y. Lee, Y. S. Ihn, and Z. Kim, Quantum illumination via quantum-enhanced sensing, Phys. Rev. A 103, 012411 (2021).
  19. H. Yang, W. Roga, J. D. Pritchard, and J. Jeffers, Gaussian state-based quantum illumination with simple photodetection, Opt. Express 29, 8199 (2021).
  20. S. Pirandola, Quantum Reading of a Classical Digital Memory, Phys. Rev. Lett. 106, 090504 (2011).
  21. I. S. Merrill, Introduction to Radar Systems (McGraw-Hill, New York, 1981).
  22. J. I. Marcum, Statistical Theory of Target Detection by Pulsed Radar: Mathematical Appendix, RAND Corporation, Santa Monica, CA, Research Memorandum RM-753, July 1, 1948. Reprinted in IRE Trans. Info. Theory IT-6, 59 (1960).
  23. W. Albersheim, A closed-form approximation to Robertson's detection characteristics, Proc. IEEE 69, 839 (1981).
  24. We work in the standard quantum optics notation, so the annihilation operator reads â=(q̂+ip̂)/2 in terms of the quadratures q̂ (position) and p̂ (momentum), with [q̂,p̂]=i. This means that the amplitude reads α=(q+ip)/2, so the mean value is given by x¯=(q,p)T=2(Reα,Imα)T. Then, the number operator takes the form n̂:=â†â=(q̂2+p̂2−1)/2, implying that a displaced and q- (or p-)squeezed state has mean number of photons n¯=(〈q̂2〉+〈p̂2〉−1)/2=|α|2+[var(q̂)+var(p̂)−1]/2. Finally, note that the quadrature variance of a thermal state corresponds to n¯+1/2, where n¯ is the mean number of photons and 1/2 is the vacuum shot noise.
  25. Note that, in general, we write r−≤r≤r+, where r+:=2n¯S+1+2n¯S(n¯S+1)≥1. However, since we consider position squeezing in our analysis, we implicitly have r≤1, so the upper bound r+ is just replaced by 1.
  26. Recall that, for a Gaussian g(z)=(σ2π)−1exp[−(z−z¯)2/(2σ2)] we have ∫t+∞g(z)dz=(1−Ω)/2 and ∫−∞tg(z)dz=(1+Ω)/2 where Ω:=erf[(t−z¯)/(σ2)].
  27. S. Pirandola, Limits and security of free-space quantum communications, Phys. Rev. Research 3, 013279 (2021).
  28. E.-L. Miao, Z.-F. Han, S.-S. Gong, T. Zhang, D.-S. Diao, and G.-C. Guo, Background noise of satellite-to-ground quantum key distribution, New J. Phys. 7, 215 (2005).
  29. C. Liorni, H. Kampermann, and D. Bruß, Satellite-based links for quantum key distribution: beam effects and weather dependence, New J. Phys. 21, 093055 (2019).
  30. See https://github.com/softquanta/squeezed_radar for the Mathematica file.
  31. G. Spedalieri, L. Piersimoni, O. Laurino, S. L. Braunstein, and S. Pirandola, Detecting and tracking bacteria with quantum light, Phys. Rev. Research 2, 043260 (2020).
  32. G. Spedalieri and S. L. Braunstein, Asymmetric quantum hypothesis testing with Gaussian states, Phys. Rev. A 90, 052307 (2014).
  33. K. Li, Second-order asymptotics for quantum hypothesis testing, Ann. Stat. 42, 171 (2014).

Outline

Information

Phys. Rev. Research 3, L042039– Published 10 December, 2021
  • Received 10 August 2021
  • Accepted 18 November 2021
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