Abstract
The analysis of accuracy for arbitrary number N copies of identical prepared samples has been performed based on Bayesian framework. The time accuracies for even superposition of coherent states (SCSs) and odd SCSs could only achieve standard quantum limit for average photon number n (or α 2) is larger. The accuracies are also deduced from the approach of Cramér-Rao bound. It can be seen from the comparison that the accuracies derived from two methods in agreement with each other when n is large. The even SCSs could provide higher precision than classical coherent states in the interval 0.7≤n≤3.
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References
Johannessen, S.: IEEE Control Syst. Mag. 24(2), 61–69 (2004)
Lewandowski, W., Azoubib, J., Klepczynski, W.J.: Proc. IEEE 87(1), 163–172 (1999)
Eddington, A.S.: The Mathematical Theory of Relativity. Cambridge University Press, Cambridge (1924)
Einstein, A.: Ann. Phys. 17, 891–921 (1905)
Jozsa, R., Abrams, D.S., Dowling, J.D., Williams, C.P.: Phys. Rev. Lett. 85, 2010–2013 (2000)
Chuang, I.L.: Phys. Rev. Lett. 85, 2006–2009 (2000)
Yurtsever, U., Dowling, J.P.: Phys. Rev. A 65, 052317 (2002)
Bahder, T.B., Golding, W.M.: Seventh International Conference on Quantum Communication, Measurement and Computing. AIP Conference Proceeding, vol. 734, pp. 395–398 (2004)
Giovannetti, V., Lloyd, S., Maccone, L.: Phys. Rev. A 70, 043808 (2004)
Giovannetti, V., Lloyd, S., Maccone, L., Wong, F.N.C.: J. Opt. B, Quantum Semiclass. Opt. 4, 415–417 (2002)
de Burgh, M., Bartlett, S.D.: Phys. Rev. A 72, 042301 (2005)
Ben-Av, R., Exman, I.: Phys. Rev. A 84, 014301 (2011)
Krco, M., Paul, P.: Phys. Rev. A 66, 024305 (2002)
Valencia, A., Scarcelli, G., Shin, Y.: Appl. Phys. Lett. 85, 2655–2657 (2004)
Ho, C., Lamas-Linares, A., Kurtsiefer, C.: New J. Phys. 11, 045011 (2009)
Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, Berlin (2004)
Giovannetti, V., Lloyd, S.: Science 306, 1330–1336 (2004)
Weinstein, J.D., Beloy, K., Derevianko, A.: Phys. Rev. A 81, 030302 (2010)
Lee, C.-W., Jeong, H.: Phys. Rev. A 80, 052105 (2009)
Stobińska, M., Jeong, H., Ralph, T.C.: Phys. Rev. A 75, 052105 (2007)
Ralph, T.C., Gilchrist, A., Milburn, G.J., Munro, W.J., Glancy, S.: Phys. Rev. A 68, 042319 (2003)
Jeong, H., Kim, M.S.: Phys. Rev. A 65, 042305 (2002)
Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J., Grangier, P.: Science 312(5770), 83–86 (2006)
Cramér, H.: Mathematical Methods of Statistics. Princeton University Press, Princeton (1946)
Giovannetti, V., Lloyd, S., Maccone, L.: Nat. Photonics 5, 222–229 (2011)
Bagan, E., Monras, A., Muñoz-Tapia, R.: Phys. Rev. A 71, 062318 (2005)
Holevo, A.S.: in Lect. Notes Maths, vol. 1055, 153 (1984)
Yuming, J., et al.: The Utility Table of Integrals. University of China Sci. & Technol. Press, Hefei (2006)
Braunstein, S.L., Caves, C.M.: Phys. Rev. Lett. 72, 3439–3443 (1994)
Boixo, S., Datta, A., et al.: Phys. Rev. A 80, 032103 (2009)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 61075014), the Science Foundation of Xi’an University of Posts and Telecommunications for Young teachers (Grant No. ZL2010-11), and the Science Foundation of Shaanxi Provincial Department of Education (Grant No. 11JK0916).
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Xie, D., Peng, Jy. & Zhao, J. Time Accuracy for Superposition of Coherent States in Quantum Clock Synchronization. Int J Theor Phys 51, 3627–3636 (2012). https://doi.org/10.1007/s10773-012-1249-9
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DOI: https://doi.org/10.1007/s10773-012-1249-9