Some Charicteristics and Applications for Quantum Information

Bi Qiao, Jinqing Fang, Harry E. Ruda

China Institute of Atomic Energy, P.O.Box 275-81, Beijing, China.
Department of Physical Science and Technology, Science School, Wuhan University of Technology, Wuhan, China.
The Center of Advanced Nanotechnology, University of Toronto, Toronto, Canada.

DOI: 10.4236/jmp.2012.39141                

Abstract

In this work some charicteristics and applications for quantum information is revealed. The various dynamical equations of quantum information density have been investigated, transmission characteristics of the dynamical mutual information have been studied, and the decoherence-free controlling procedure has been considered, which exposes that quantum information is holographic through the similarity structure of subdynamic kinetic equations for quantum information density.

Keywords

Quantum Information; Dynamical Equation; Density Operator

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. R. Simon, “On the Power of Quantum Computation,” SIAM Journal on Computing, Vol. 26, No. 5, 1997, pp. 1474-1483. doi:10.1137/S0097539796298637
[2]	P. W. Shor, “Polynomial-Time Algorithms for Prime Fac- torization and Discrete Logarithms on a Quantum Computer,” SIAM Journal on Computing, Vol. 26, No. 5, 1997, pp. 1484-1509. doi:10.1137/S0097539795293172
[3]	S. Wiesner, “Conjugate Coding,” SIGACT News, Vol. 15, No. 1, 1983, pp. 78-88. doi:10.1145/1008908.1008920
[4]	C. Bennett, F. Bessette, G. Brassard, L. Salvail and J. Smolin, “Experimental Quantum Cryptography,” Journal of Cryptology, Vol. 5, No. 1, 1993, pp. 3-28. doi:10.1007/BF00191318
[5]	P. W. Shor, “Algorithms for Quantum Computation: Discrete Logarithms and Factoring,” Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, 1994, pp. 124-134. doi:10.1109/SFCS.1994.365700
[6]	D. Deutch, “Quantum Computational Networks,” Proceedings of the Royal Society A, Vol. 425, No. 1868, 1985, pp. 73-90. doi:10.1098/rspa.1989.0099
[7]	L. Grover, “A Fast Quantum Mechanical Algorithm for Database Search,” Proceedings of the 28th Annual ACM Symposium on the Theory of Computation, ACM Press, New York, 1995.
[8]	S. Tomonaga, “On a Relativistically Invariant Formation of the Quantum Theory of Wave Fields, I.,” Progress of Theoretical Physics, Vol. 1, No. 2, 1946, pp. 27-42. doi:10.1143/PTP.1.27
[9]	S. Tomonaga, “On a Relativistically Invariant Formation of the Quantum Theory of Wave Fields, II,” Progress of Theoretical Physics, Vol. 2, 1947, p. 101.
[10]	H. P. Breuer, “The Theory of Quantum Open Systems,” Oxford University Press, New York, 2002.
[11]	S. S. Schweber, “An Introduction to Relativistic Quantum Field Theory,” Row, Peterson and Company, Evanston, 1948.
[12]	J. Schwinger, “Quantum Electrodynamics. I. A Covariant Formulation,” Physical Review, Vol. 74, No. 10, 1948, pp. 1439-1461. doi:10.1103/PhysRev.74.1439
[13]	E. Prugovecki, “Principles of Quantum General Relativity,” World Scientific Publishing, Co. Pte. Ltd., Singapore, 1995.
[14]	D. Giulini, C. Kiefer and C. L?mmerzahl, “Quantum Gravity: From Theory to Experimental Search,” Springer-Verlag, New York, 2003.
[15]	X. S. Xing, “On Dynamical Statistical Information Theory,” Transactions of Beijing Institute of Technology (Chinese), Vol. 24, 2004.
[16]	B. Qiao, X. S. Xing and H. E. Ruda, “Dynamical Equations for Quantum Information and Application in Infor- mation Channel,” Chinese Physics Letters, Vol. 22, No. 7, 2005, p. 1618. doi:10.1088/0256-307X/22/7/016
[17]	M. Ohya and D. Petz, “Quantum Entropy and Its Use,” Springer-Verlag/Heidelberg, Berlin/New York, 2004.
[18]	H. J. Carmichael, “Statistical Methods in Quantum Optics 1, Master Equations and Fokker-Planck Equations,” Springer-Verlag/Heidelberg, Berlin/New York, 1999.
[19]	C. Arndt, “Information Measures, Information and Its Description in Science and Engineering,” Springer-Ver- lag/Heidelberg, Berlin/New York, 2001.
[20]	I. Antoniou and S. Tasaki, “Generalized Spectral De- compositions of Mixing Dynamical Systems,” International Journal of Quantum Chemistry, Vol. 46, No. 3, 1993, pp. 425-474. doi:10.1002/qua.560460311
[21]	T. Petrosky and I. Prigogine, “Alternative Formulation of Classical and Quantum Dynamics for Non-Integrable Systems,” Physica A: Statistical Mechanics and Its Applications, Vol. 175, No. 1, 1991, pp. 146-209. doi:10.1016/0378-4371(91)90273-F
[22]	I. Antoniou, Y. Melnikov and B. Qiao, “Master Equation for a Quantum System Driven by a Strong Periodic Field in the Quasienergy Representation,” Physica A: Statistical Mechanics and Its Applications, Vol. 246, No. 1-2, 1997, pp. 97-114. doi:10.1016/S0378-4371(97)00343-9
[23]	B. Qiao, H. E. Ruda, M. S. Zhang and X. H. Zeng, “Kinetic Equation, Non-Perturbative Approach and Decoherence Free Subspace for Quantum Open System,” Physica A: Statistical Mechanics and Its Applications, Vol. 322, 2003, pp. 345-358. doi:10.1016/S0378-4371(02)01809-5
[24]	B. Qiao, H. E. Ruda and Z. D. Zhou, “Dynamical Equations of Quantum Information and Gaussian Channel,” Physica A: Statistical Mechanics and Its Applications, Vol. 363, No. 2, 2006, pp. 198-210. doi:10.1016/j.physa.2005.08.044
[25]	R. Balescu, “Equilibrium and Non-Equilibrium Statistical Mechanics,” Wiley, New York, 1975.
[26]	S. Nakajima, “On Quantum Theory of Transport Phenomena,” Progress of Theoretical Physics, Vol. 20, No. 6, 1958, pp. 948-959. doi:10.1143/PTP.20.948
[27]	R. Zwanzig, “Ensemble Method in the Theory of Irreversibility,” Journal of Chemical Physics, Vol. 33, No. 5, 1960, pp. 1338-1341. doi:10.1063/1.1731409
[28]	S. Chapman, “Kinetic Theory of Simple and Composite Monatomic Gases: Viscosity, Thermal Conduction, and Diffusion,” Proceedings of the Royal Society of London. Series A, Vol. 93, No. 646, 1916, pp. 1-20. doi:10.1098/rspa.1916.0046
[29]	D. Enskog, “Kinetische Theorie der Vorg?ng in M?ssig verdünnten Gasen,” Almqvist and Wiksells, Uppsala, 1917.
[30]	N. N. Bogoliubov, “Kinetic Equations,” Journal of Physics-USSR, Vol. 10, No. 256, 1946, p. 265.
[31]	M. Born and H. S. Green, “A General Kinetic Theory of Liquids,” Cambridge University Press, Cambridge, 1949.
[32]	J. G. Kirkwood, “The Statistical Mechanical Theory of Transport Processes I. General Theory,” Journal of Chemical Physics, Vol. 14, No. 3, 1946, p. 180. doi:10.1063/1.1724117
[33]	J. G. Kirkwood, “Selected Topics in Statistical Mechanics,” I. Oppenheim, Ed., Gordon and Breach, New York, 1967.
[34]	J. Yvon, “La Theorie Statistiques des Fluides et l’Equa- tion d’Etat, Herman et Cie, Paris, 1935.
[35]	M. S. Green, “Markoff Random Processes and the Statis- tical Mechanics of Time—Dependent Phenomena. II. Irreversible Processes in Fluids,” Journal of Chemical Physics, Vol. 20, No. 3, 1954, pp. 398-413.
[36]	R. Kubo, “Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems,” Journal of the Physical Society of Japan, Vol. 12, 1957, pp. 570-586. doi:10.1143/JPSJ.12.570
[37]	H. Mori, “Statistical-Mechanical Theory of Transport in Fluids,” Physical Review, Vol. 112, 1958, pp. 1829-1842. doi:10.1103/PhysRev.112.1829
[38]	H. Mori, “Correlation Function Method for Transport Phenomena,” Physical Review, Vol. 115, 1959, pp. 298-300. doi:10.1103/PhysRev.115.298
[39]	D. Zubarev, V. Morozov and G. R?pke, “Statistical Mechanics of Nonequilibrium Processes,” Akademie Verlag, Berlin, 1996.
[40]	R. Luzzi, á. R. Vasconcellos and J. G. Ramos, “Predictive Statistical Mechanics—A Non-Equilibrium Ensemble Formalism,” Kluwer Academic Publishers, Dordrecht, 2002.
[41]	B. C. Eu, “Nonequilibrium Statistical Mechanics (Ensemble Method),” Kluwer Academic Publishers, Dordrecht/Boston/London, 1998.
[42]	X. S. Xing, “On Non Equilibrium Statistical Physics— Concurrently on the Fundamental Equation of Nonequilibrium Entropy,” Scientia Sinica Physica, Mechanica & Astronomica, Vol. 40, No. 12, 2011, pp. 1441-1660.
[43]	B. Qiao, H. E. Ruda, X. H. Zeng and B. B. Hu, “Extended Space for Quantum Cryptography Using Mixed States,” Physica A: Statistical Mechanics and Its Applications, Vol. 320, 2003, pp. 357-370. doi:10.1016/S0378-4371(02)01539-X
[44]	B. Qiao, L. Guo and H. E. Ruda, “Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation,” Advances in Mathematical Physics, Vol. 2010, 2010, Article ID: 365653.