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Estimating the angular dynamics of a fan window stroboscope from noisy quantum image measurements

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Abstract

In this paper, we first formulate the dynamics of the fan motor rotation angle \(\theta (t)\) in terms of a second-order Ito-stochastic differential equation (s.d.e). The aim is to estimate \(\theta (t)\) on a real-time basis by taking measurements of the transition probability of a quantum system from one state to another when excited by a quantum image field that passes through the fan stroboscopic window. The quantum image field is modeled as a superposition of creation and annihilation operators modulated by appropriate functions of time, dependent upon the quantum electromagnetic field frequency. This field after stroboscopic windowing excites a 3-D quantum oscillator which causes it to make transitions between two oscillator base states with the Quantum field remaining in a coherent state. The dynamics of the transition probability between two fixed oscillator states is shown to be a component of a \(5\times 1\) vector that satisfies an s.d.e in which the fan window angle and the fan window angular velocity also form some components. Simulation displays the evolution of these transition probabilities as well as of the fan rotation angle. This s.d.e for the \(5\times 1\) vector when coupled to a measurement model for the 5th component, namely the transition probability, is directly substituted into the equations for an extended Kalman filter (E.K.F), thereby obtaining real-time estimates of the fan angle in terms of the accumulated data of oscillator transition probability.

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References

  1. Grabert, H., Hänggi, P., Talkner, P.: Is quantum mechanics equivalent to a classical stochastic process? Phys. Rev. A 19, 2440 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  2. Sozzo, S.: The quantum harmonic oscillator in the ESR model. Found. Phys. 43(6), 792–804 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Kumar, M., Chakravorty, S.: A Nonlinear Filter Based on Fokker–Planck Equation. American Control Conference Marriott Waterfront, Baltimore (2010)

    Book  Google Scholar 

  4. Amir, A., Lahini, Y., Perets, H.B.: Classical diffusion of a quantum particle in a noisy environment. Phys. Rev. E 79, 050105(R) (2009)

    Article  ADS  Google Scholar 

  5. Kushner, H.J.: On the differential equations satisfied by conditional probability densities of Markov processes (with applications). J. SIAM Control 2, 106–119 (1964)

    MATH  Google Scholar 

  6. Hahne, G.E.: Bidirectional Classical Stochastic Processes with Measurements and Feedback. NASA Ames Research Center, TNA, Moffett Field (2005)

    Google Scholar 

  7. Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic Press, New York (1970)

    MATH  Google Scholar 

  8. Ito, K.: Approximations of a stochastic evolution equations. Proc. IEEE Conf. Decis. Control 4, 4035–4040 (1995)

    Google Scholar 

  9. Gillespie, D.T., Alltop, W.O., Martin, J.M.: Modeling quantum measurement probability as a classical stochastic process. Chaos 11(3), 548 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Neergaard-Nielsen, J.S., Nielsen, B.M., Mølmer, K., Polzik, E.S.: Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett. 97, 083604 (2006)

    Article  ADS  Google Scholar 

  11. Gough, J., Kostler, C.: Quantum filtering in coherent states. Commun. Stoch. Anal. 4(4), 505–521 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Gough, J.E., James, M.R., Nurdin, H.I., Combes, J.: Quantum filtering for systems driven by fields in single-photon states or superposition of coherent states. Phys. Rev. A 86, 043819 (2012)

    Article  ADS  Google Scholar 

  13. Doherty, A.C., Jacobs, K.: Feedback control of quantum systems using continuous state estimation. Phys. Rev. A At. Mol. Opt. Phys. 60(4), 2700–2711 (1999)

    Article  ADS  Google Scholar 

  14. Sage, A.P., Melsa, M.L.: Estimation Theory with Applications to Communications and Control. McGraw-Hill, New York (1971)

    MATH  Google Scholar 

  15. Emzir, M.F., Woolley, M.J., Petersen, I.R.: A quantum extended filter. J. Phys. A Math. Theor. 50(22), 225301 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Ito, K.: Gaussian filter for non-linear filtering problems. Proc. IEEE Conf. Decis. Control 2, 1218–1223 (2000)

    Google Scholar 

  17. Jazwinski, A.H.: Filtering for non-linear dynamical systems. IEEE Trans. Autom. Control 11, 612–622 (1966)

    Article  Google Scholar 

  18. Kushner, H.J.: Approximation to optimal non-linear filters. IEEE Trans. Autom. Control 12, 546–556 (1967)

    Article  Google Scholar 

  19. Kushner, H.J.: Dynamical equations for optimal nonlinear filtering. J. Differ. Equ. 3, 179–190 (1967)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Yamamoto, N.: Robust observer for uncertain linear quantum systems. Phys. Rev. A At. Mol. Phys. 74, 032107 (2006)

    Article  ADS  Google Scholar 

  21. Vergez, P., Sauter, L., Dalke, S.: An improved Kalman filter for satellite orbit predictions. J. Astronaut. Sci. 52, 1–22 (2004)

    MathSciNet  Google Scholar 

  22. Carrassi, A., Vannitsem, S.: State and parameter estimation with the extended Kalman filter: an alternative formulation of the model error dynamics. Q. J. R. Meteorol. Soc. 137, 435–451 (2011)

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Multimedia Research Laboratory, Room No. 201, Block IV ECE Division, Netaji Subhas Institute of Technology, Sector-3, Dwarka, New Delhi, 110078, India

    Rohit Singh, Jyotsna Singh & Harish Parthasarathy

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  1. Rohit Singh
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  2. Jyotsna Singh
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  3. Harish Parthasarathy
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Correspondence to Jyotsna Singh.

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Singh, R., Singh, J. & Parthasarathy, H. Estimating the angular dynamics of a fan window stroboscope from noisy quantum image measurements. Quantum Inf Process 17, 227 (2018). https://doi.org/10.1007/s11128-018-2000-0

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  • DOI: https://doi.org/10.1007/s11128-018-2000-0

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