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Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing (2402.17922v1)

Published 27 Feb 2024 in quant-ph, cs.IT, math.IT, math.ST, and stat.TH

Abstract: Quantum Cram\'er-Rao bound is the ultimate limit of the mean squared error for unbiased estimation of an unknown parameter embedded in a quantum state. While it can be achieved asymptotically for large number of quantum state copies, the measurement required often depends on the true value of the parameter of interest. This paradox was addressed by Hayashi and Matsumoto using a two-stage approach in 2005. Unfortunately, their analysis imposes conditions that severely restrict the class of classical estimators applied to the quantum measurement outcomes, hindering applications of this method. We relax these conditions to substantially broaden the class of usable estimators at the cost of slightly weakening the asymptotic properties of the two-stage method. We apply our results to obtain the asymptotics of quantum-enhanced transmittance sensing.

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References (25)
  1. H. Nagaoka, “An asymptotically efficient estimator for a one-dimensional parametric model of quantum statistical operators,” in Proc. IEEE Int. Symp. Inf. Theory, vol. 198, 1988.
  2. A. Fujiwara, “Strong consistency and asymptotic efficiency for adaptive quantum estimation problems,” J. Phys. A: Math. Gen., vol. 39, no. 40, p. 12489, 2006.
  3. R. D. Gill and S. Massar, “State estimation for large ensembles,” Phys. Rev. A, vol. 61, p. 042312, Mar. 2000.
  4. M. Hayashi and K. Matsumoto, “Statistical model with measurement degree of freedom and quantum physics,” in Asymptotic theory of quantum statistical inference: selected papers.   World Scientific, 2005, pp. 162–169.
  5. W. K. Newey and D. McFadden, “Chapter 36 large sample estimation and hypothesis testing,” in Handbook of Econometrics, ser. Handbooks in Economics.   Elsevier, 1994, vol. 4, pp. 2111–2245.
  6. Z. Gong, C. N. Gagatsos, S. Guha, and B. A. Bash, “Fundamental limits of loss sensing over bosonic channels,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT), virtual, Jul. 2021.
  7. Z. Gong, N. Rodriguez, C. N. Gagatsos, S. Guha, and B. A. Bash, “Quantum-enhanced transmittance sensing,” IEEE J. Sel. Topics Signal Process., vol. 17, no. 2, pp. 473–490, 2023.
  8. H. Nagaoka, “A new approach to Cramér-Rao bounds for quantum state estimation,” in Asymptotic Theory of Quantum Statistical Inference: Selected Papers.   World Scientific, 2005, pp. 100–112.
  9. H. Nagaoka, “On the parameter estimation problem for quantum statistical models,” in Asymptotic Theory of Quantum Statistical Inference: Selected Papers.   World Scientific, 2005, pp. 125–132.
  10. R. Jonsson and R. D. Candia, “Gaussian quantum estimation of the loss parameter in a thermal environment,” J. Phys. A: Math. Theor., vol. 55, no. 38, p. 385301, Aug. 2022.
  11. R. Nair and M. Gu, “Fundamental limits of quantum illumination,” Optica, vol. 7, no. 7, pp. 771–774, Jul. 2020.
  12. S. Lloyd, “Enhanced sensitivity of photodetection via quantum illumination,” Science, vol. 321, no. 5895, pp. 1463–1465, 2008.
  13. 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., vol. 101, p. 253601, Dec. 2008.
  14. S. Guha and B. I. Erkmen, “Gaussian-state quantum-illumination receivers for target detection,” Phys. Rev. A, vol. 80, p. 052310, Nov. 2009.
  15. J. H. Shapiro, “The quantum illumination story,” IEEE Aerosp. Electron. Syst. Mag., vol. 35, no. 4, pp. 8–20, 2020.
  16. M. Sanz, U. Las Heras, J. J. García-Ripoll, E. Solano, and R. Di Candia, “Quantum estimation methods for quantum illumination,” Phys. Rev. Lett., vol. 118, p. 070803, Feb. 2017.
  17. T. Tan, K. K. Lee, A. Ashok, A. Datta, and B. A. Bash, “Robust adaptive quantum-limited super-resolution imaging,” in Proc. Asilomar Conf. Signals Syst. Comput., Pacific Grove, CA, USA, Nov. 2022.
  18. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys., vol. 84, pp. 621–669, May 2012.
  19. S. Guha, “Classical capacity of the free-space quantum-optical channel,” Master’s thesis, Massachusetts Institute of Technology, 2004.
  20. S.-H. Chang, P. C. Cosman, and L. B. Milstein, “Chernoff-type bounds for the Gaussian error function,” IEEE Trans. Commun., vol. 59, no. 11, pp. 2939–2944, 2011.
  21. P. J. Huber et al., “The behavior of maximum likelihood estimates under nonstandard conditions,” in Proc. 5th Berkeley Symp. Math. Statist. Prob., vol. 5, no. 1, Berkeley, CA, USA, 1967, pp. 221–233.
  22. G. Tauchen, “Diagnostic testing and evaluation of maximum likelihood models,” J. Econom., vol. 30, no. 1-2, pp. 415–443, 1985.
  23. User “stevecheng (10074)”, “Differentiation under the integral sign,” https://planetmath.org/differentiationundertheintegralsign, Mar. 23, 2013, (accessed 24 February 2024).
  24. E. Talvila, “Necessary and sufficient conditions for differentiating under the integral sign,” Am. Math. Mon., vol. 108, no. 6, pp. 544–548, 2001.
  25. L. Mirsky, “A trace inequality of john von neumann,” Monatshefte für mathematik, vol. 79, no. 4, pp. 303–306, 1975.
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