Abstract
We estimate the quantum state of two qubits and a two-mode field obeying the Gaussian distribution and give the two Gaussian modes and the density matrix in explicit forms. We study the dynamic properties of the Mandel parameter as a quantifier of the statistical properties for the radiation field during the process of its time evolution. We investigate the nonlocal correlation between the two atoms as well as their entanglement with the field distribution. In addition, we obtain the Fisher information based on the estimation of the atomic state and compare it with the Mandel parameter. Finally, we explore the link between the statistical quantities of the field for different parameters of the two Gaussian modes.
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References
R. A. Fisher, Proc. Cambridge Philos. Soc., 22, 700 (1929); reprinted in: J. H. Bennett (Ed.), Collected Papers of R. A. Fisher, University of Adelaide Press, South Australia (1972), pp. 15–40.
V. Giovannetti, S. Lloyd, and L. Maccone, Science, 306, 1330 (2004).
J. Dowling, Contemp. Phys., 49, 125 (2008).
J. A. Jones, S. D. Karlen, J. Fitzsimons, et al., Science, 324, 1166 (2009).
S. Simmons, J. A. Jones, S. D. Karlen, et al., Phys. Rev. A, 82, 022330 (2010).
B. L. Higgins, D. W. Berry, S. D. Bartlett, et al., Nature, 450, 393 (2007).
U. Dorner, B. J. Smith, J. S. Lundeen, et al., Phys. Rev. A, 80, 013825 (2009).
H. Cramer, Mathematical Methods of Statistics, Princeton University Press (1946).
U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, et al., Phys. Rev. Lett., 102, 040403 (2009).
S. Abdel-Khalek, Int. J. Quantum Inf., 7, 1541 (2009)
J. Joo, W. J. Munro, and T. P. Spiller, Phys. Rev. Lett., 107, 083601 (2011).
R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, et al., Phys. Rev. A, 80, 013825 (2009).
P. Facchi, R. Kulkarni, V. I. Man’ko, et al., Phys. Lett. A, 374, 4801 (2010).
M. Tavis and F. W. Cummings, Phys. Rev. A, 170, 379 (1968).
S. Abdel-Khalek, Open Syst. Inform. Dyn., 22, 1550015 (2015).
J. H. Eberly and T. Yu, Science, 316, 555 (2007).
A.-S. F. Obada, S. Abdel-Khalek, and D. A. M. Abo-Kahla, Opt. Commun., 283, 662 (2010).
A. S.-F. Obada and S. Abdel-Khalek, Physica A, 389, 891 (2010).
H. H. Abu-Zinadah and S. Abdel-Khalek, Res. Phys., 7, 4318 (2017).
D. McHugh, M. Ziman, and V. Bužek, Phys. Rev. A, 74, 042303 (2006).
B. R. Frieden, Physics from Fisher Information, Cambridge University Press (2010).
D. A. Lavis and R. F. Streater, Studies History Philos. Mod. Phys., 33, 327 (2002).
F. Pennini and A. Plastino, Phys. Lett. A, 326, 20 (2004).
A. S. Obada and S. Abdel-Khalek, J. Phys. A: Math. Gen., 37, 6573 (2004).
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press (1995).
V. V. Dodonov and V. I. Man’ko, Theory of Nonclassical States of Light, CRC Press, 1st ed. (2003).
M. A. Alsahhaf, S. A. Aldaghfag, and S. Abdel-Khalek, J. Russ. Laser Res., 38, 437 (2017).
M. A. Eman Hilal and S. Abdel-Khalek, J. Russ. Laser Res., 39, 12 (2018).
J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955).
S. J. D. Phoenix and P. L. Knight, Ann. Phys., 186, 381 (1988).
K. Berrada, S. Abdel-Khalek, and A. Eied, J. Russ. Laser Res., 37, 45 (2016).
G. Vidal and R. F. Werner, Phys. Rev. A, 65, 032314 (2002).
K. Berrada, S. Abdel-Khalek, and A.-S. F. Obada, Phys. Lett. A, 376, 1412 (2012).
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Momenkhan, F.A., Abdel-Khalek, S. Fisher Information and Statistical Properties of Two Qubits in Two Modes of the Gaussian Distribution. J Russ Laser Res 39, 216–221 (2018). https://doi.org/10.1007/s10946-018-9711-7
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DOI: https://doi.org/10.1007/s10946-018-9711-7