Abstract
Realistic quantum systems are still an open area for more studies in the field of quantum information and its applications. Therefore, the interaction between the external environment and quantum systems, understanding the dynamics of different information quantifiers, and finding the correlation between different phenomena may stimulate great interest. In this regard, the information flow and phase space entropy of a quantum system is a potential resource for quantum information processing. We investigate the relationship between the quantum Fisher information, quantum entanglement and bifurcations of the Husimi Q-function, and the Wehrl phase distribution of a single qubit system coupled to an environment. We examine the effect of qubit damping on the evolution of different quantities during the time evolution. Finally, we discuss the the link between the dynamic properties of the quantum Fisher information flow and bifurcations of the phase-space entropy.
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References
G. Schedelbeck, W. Wegscheider, M. Bichler, and G. Abstreiter, Science, 278, 1792 (1997).
D. Loss and D. P. DiVincenzo, Phys. Rev. A, 57, 120 (1998).
B. E. Kane, Nature, 393, 133 (1998).
D. P. Divincenzo, Fortschr. Phys., 48, 771 (2000).
T. P. Orlando, J. E. Mooij, L. Tian, et al., Phys. Rev. B, 60, 15398 (1999).
V. Bouchiat, D. Vion, P. Joyez, et al., Phys. Scr., T76, 165 (1998).
A. Miranowicz, J. Bajer, M. R. B. Wahiddin, and N. Imoto, J. Phys. A: Math. Gen., 34, 3887 (2001).
S. Abdel-Khalek, A. A. Mousa, and T. A. Nofal, J. Russ. Laser Res., 33, 547 (2012).
W. Leonski, A. Miranowicz, and K. Piatek, Proc. SPIE, 5259, 37 (2003).
I. Jex and A. Orlowski, J. Mod. Opt., 41, 2301 (1994).
S. Abdel-Khalek, Phys. Scr., 80, 045302 (2009).
R. Dermez and S. Abdel-Khalek, J. Russ. Laser Res., 32, 287 (2011).
A. S. F Obada, S. Abdel-Khalek, and A. Plastino, Physica A, 390, 525 (2011).
S. Abdel-Khalek and A.-S. Obada, Ann. Phys., 325, 2542 (2010).
A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).
O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 25, 115 (2004).
V. N. Chernega, O. V. Man’ko, V. I. Man’ko, et al., J. Russ. Laser Res., 27, 132 (2006).
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2000).
C. H. Bennett, G. Brassard, C. Crépeau, et al., Phys. Rev. Lett., 70, 1895 (1993).
P. Agrawal and A. Pati, Phys. Rev. A, 74, 062320 (2006).
Z.-Q. Yin, H.-W. Li, W. Chen, et al., Phys. Rev. A, 82, 042335 (2010).
T.-G. Noh, Phys. Rev. Lett., 103, 230501 (2009).
K. Berrada, S. Abdel-Khalek, and C. H. R. Ooi, Phys. Rev. A, 86, 033823 (2012).
H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control, Cambridge University Press (2009).
K. Berrada, F. F. Fanchini, and S. Abdel-Khalek, Phys. Rev. A, 85, 052315 (2012).
S. Popescu and D. Rohrlich, Phys. Rev. A, 56, R3319 (1997).
J. V. Neumann, Mathematical Foundations of Quantum Mechanics, Investigations in Physics, Princeton University Press (1955).
C. E. López, G. Romero, F. Lastra, et al., Phys. Rev. Lett., 101, 080503 (2008).
E. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89 (1963).
S. M. Barnett and P. L. Knight, Phys. Rev. A, 33, 2444 (1986).
R. R. Puri and G. S. Agarwal, Phys. Rev. A, 35, 3433 (1987).
T. Quang, P. L. Knight, and V. Bužek, Phys. Rev. A, 44, 6092 (1991).
J. Eiselt and H. Risken, Phys. Rev. A, 43, 346 (1991).
B.-G. Englert, M. Naraschewski, and A. Schenzle, Phys. Rev. A, 50, 2667 (1994).
S. Glazek, “Limit cycles in quantum mechanics,” in: J. Asch and A. Joye (Eds.), Mathematical Physics of Quantum Mechanics, Lecture Notes in Physics, Springer Berlin/Heidelberg (2006), Vol. 690, p. 65.
K. R. Schneider, B. Wegner, and J. Toth, J. Math. Chem., 1, 219 (1987).
O. Gurel, Biosyst., 7, 83 (1975).
S. Sastry, Nonlinear systems. Analysis, Stability, and Control, Interdisciplinary Applied Mathematics, Springer, New York (1999).
E. O. Abdel-Rahman, Algorithmic Contributions to the Qualitative Analysis of Autonomous Parametric Dynamical Systems, Lambert Academic Publishing (2011).
T. Gevorgyan and G. Kryuchkyan, Phys. Part. Nucl. Lett., 8, 473 (2011).
J. Dajka and J. Luczka, J. Phys. A: Math. Theor., 41, 442001 (2008).
D. Meschede, H. Walther, and G. Müller, Phys. Rev. Lett., 54, 551 (1985).
B. W. Shore and P. L. Knight, J. Mod. Opt., 40, 1195 (1993).
S. Abdel-Khalek, E. Edfawy, and M. S. Almalki, J. Comput. Theor. Nanosci., 11, 1499 (2014).
A. S. F. Obada, S. Abdel-Khalek, and M. E. Shaheen, Appl. Math. Inform. Sci., 8, 1167 (2014).
E. Wigner, Phys. Rev., 40, 749 (1932).
K. E. Cahill and R. Glauber, Phys. Rev., 177, 1882 (1969).
E. L. Bolda, S. M. Tan, and D. F. Walls, Phys. Rev. A, 57, 4686 (1998).
A. Wehrl, Rep. Math. Phys., 16, 353 (1979).
V. Perinov, J. Krepelka, J. Perina, et al., Optica Acta: Int. J. Opt., 33, 15 (1986).
C. Perez-Campos, J. R. Gonzlez-Alonso, O. Castanos, and R. Lopez-Pea, Ann. Phys., 325, 325 (2010).
S. Abdel-Khalek, Int. J. Quantum Inform., 7, 1541 (2009).
A. Orlowski, H. Paul, and G. Kastelewicz, Phys. Rev. A, 52, 1621 (1995).
J. A. Jones, S. D. Karlen, J. Fitzsimons, 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, H. M. Bartlett, et al., Nature, 450, 393 (2007).
R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, Phys. Rev. A, 80, 013825 (2009).
R. A. Fisher, Math. Proc. Cambridge Philos. Soc., 22, 700 (1925).
H. Cramer, Mathematical Methods of Statistics. (PMS-9), Princeton University Press (1999).
U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, et al., Phys. Rev. Lett., 102, 040403 (2009).
V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett., 96, 010401 (2006).
J. Joo, W. J. Munro, and T. P. Spiller, Phys. Rev. Lett., 107, 083601 (2011).
K. Modi, H. Cable, M. Williamson, and V. Vedral, Phys. Rev. X, 1, 021022 (2011).
L. Henderson and V. Vedral, J. Phys. A: Math. Gen., 34, 6899 (2001).
H. Ollivier and W. H. Zurek, Phys. Rev. Lett., 88, 017901 (2001).
K. Nagata, Int. J. Theor. Phys., 48, 3353 (2009).
S. Abdel-Khalek, Quantum Inform. Process., 12, 3761 (2013).
G. Vidal and R. F. Werner, Phys. Rev. A, 65, 032314 (2002).
K. Berrada, S. Abdel-Khalek, and A.-S. Obada, Phys. Lett. A, 376, 1412 (2012).
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Abdel-Rahman, E.O., Malki, Z.S.A. & Abdel-Khalek, S. Fisher Information Flow and Bifurcation Properties of Wehrl Entropy of a Single Qubit System Under the Damping Effect. J Russ Laser Res 35, 590–601 (2014). https://doi.org/10.1007/s10946-014-9466-8
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DOI: https://doi.org/10.1007/s10946-014-9466-8