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Nonclassicality of states and measurements by breaking classical bounds on statistics

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Publication Date
2009-04-24
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Rivas, Ángel
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American Physical Society
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We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum, and definite conclusions are obtained without evaluation of moments or any other more sophisticated procedures. These nonclassical tests are independent of other typical quantum signatures such as sub-Poissonian statistics, quadrature squeezing, or oscillatory statistics. This approach can be equally well applied to very diverse situations such as single- and two-mode fields, observables with continuous and discrete spectra, finite- and infinite-dimensional systems, and ideal and noisy measurements.
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©2009 The American Physical Society. We thank Dr. Shashank Virmani for fruitful discussions and Professor Mark Hillery for valuable comments. A.R. acknowledges financial support from the University of Hertfordshire and the EU Integrated Project QAP. A.L. acknowledges support from Project No. FIS2008-01267 of the Spanish Dirección General de Investigación del Ministerio de Ciencia e Innovación.
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[1] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, England, 1995); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997); V. V. Dodonov, J. Opt. B: Quantum Semiclassical Opt. 4, R1 (2002); U. M. Titulaer and R. J. Glauber, Phys. Rev. 140, B676 (1965); L. Mandel, Phys. Scr. T12, 34 (1986); D.-G. Welsch, W. Vogel, and T. Opatrný, in Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1999), Vol. 39; T. Richter and W. Vogel, Phys. Rev. Lett. 89, 283601 (2002); E. V. Shchukin and W. Vogel, Phys. Rev. A 72, 043808 (2005); R. Alicki and N. Van Ryn, J. Phys. A 41, 062001 (2008). [2] M. Hillery, Phys. Rev. A 35, 725 (1987). [3] H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977); R. Short and L. Mandel, ibid. 51, 384 (1983); R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, ibid. 55, 2409 (1985). [4] D. N. Klyshko, Phys. Lett. A 213, 7 (1996); C. T. Lee, Phys. Rev. A 55, 4449 (1997). [5] G. S. Agarwal and K. Tara, Phys. Rev. A 46, 485 (1992); A. Zavatta, V. Parigi, and M. Bellini, ibid. 75, 052106 (2007); T. Kiesel, W. Vogel, V. Parigi, A. Zavatta, and M. Bellini, ibid. 78, 021804(R) (2008). [6] W. Vogel, Phys. Rev. Lett. 84, 1849 (2000); T. Richter and W. Vogel, ibid. 89, 283601 (2002); E. Shchukin, T. Richter, and W. Vogel, Phys. Rev. A 71, 011802(R) (2005); A. I. Lvovsky and J. H. Shapiro, ibid. 65, 033830 (2002). [7] R. W. Spekkens, Phys. Rev. Lett. 101, 020401 (2008). [8] A. Luis and L. L. Sánchez-Soto, Phys. Rev. Lett. 83, 3573 (1999); J. Fiurášek, Phys. Rev. A 64, 024102 (2001); H. B. Coldenstrodt-Ronge, J. S. Lundeen, K. L. Pregnell, A. Feito, B. J. Smith, W. Mauerer, Ch. Silberhorn, J. Eisert, M. B. Plenio, and I. A. Walmsley, J. Mod. Opt. 56, 432 (2009) ; J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, Ch. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, Nat. Phys. 5, 27 (2009). [9] D. R. Cox and H. D. Miller, Theory of Stochastic Processes (Chapman & Hall/CRC, London, 1977). [10] L. Liu, J. Math. Anal. Appl. 328, 1484 (2007). [11] S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A 213, 1 (1996). [12] V. Bužek and P. L. Knight, in Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1995), Vol. 34, p. 1; C. C. Gerry and P. L. Knight, Am. J. Phys. 65, 964 (1997); M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, Phys. Rev. A 45, 5193 (1992); L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 71, 2360 (1993); M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, ibid. 77, 4887 (1996); L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996); S. Haroche, Phys. Today 51 (7), 36 (1998); J. M. Raimond, M. Brune, and S. Haroche, Phys. Rev. Lett. 79, 1964 (1997); C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, Science 272, 1131 (1996); M. W. Noel and C. R. Stroud, Jr., Phys. Rev. Lett. 77, 1913 (1996); J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, Nature (London) 406, 43 (2000). [13] V. V. Dodonov, I. A. Malkin, and V. I. Man’ko, Physica 72, 597 (1974). [14] H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); B. Yurke, Phys. Rev. A 32, 311 (1985); U. Leonhardt and H. Paul, ibid. 48, 4598 (1993); T. Kim, Y. Ha, J. Shin, H. Kim, G. Park, K. Kim, T. G. Noh, and Ch. K. Hong, ibid. 60, 708 (1999). [15] A. A. Semenov, A. V. Turchin, and H. V. Gomonay, Phys. Rev. A 78, 055803 (2008). [16] For further connection between entanglement and classicality see for instance J. Sperling and W. Vogel, e-print arXiv:0811.4527. [17] F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972). [18] O. Giraud, P. Braun, and D. Braun, Phys. Rev. A 78, 042112 (2008). [19] A. Luis, Phys. Rev. A 73, 063806 (2006). [20] A. Luis, Phys. Rev. A 66, 013806 (2002). [21] A. Rivas and A. Luis, Phys. Rev. A 77, 022105 (2008).
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