Quantum information density and network

Abstract

We present a quantum information network in which quantum information density is used for performing quantum computing or teleportation. The photons are entangled in quantum channels and play a role of flying ebit to transmit interaction among the nodes. A particular quantum Gaussian channel is constructed; it permits photon-encoded information to transmit quantum signals with certain quantum parallelism. The corresponding quantum dynamical mutual information is discussed, and the controlling nodes connectivity by driving the network is studied. With regard to different driving functions, the connectivity distribution of the network is complicated. They obey positive or negative power law, and also influence the assortativity coefficient or the dynamical property of the network.

Keywords

quantum information / Gaussian channel / complex network

References

[1] J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, Phys. Rev. A, 1999, 59: 4249

[2] J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett., 1997, 78: 3221

[3] C. H. Bennett, and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, New York: IEEE, 1984

[4] C. H. Bennett, F. Bessette, G. Brassard, L. Salvai, and J. Smolin, J. Cryptology, 1992, 5: 3

[5] X.-F. Zhou, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. Lett., 2005, 71: 064302

[6] G. Bianconi and A-L Barabási, Phys. Rev. Lett., 2001, 86: 5632

[7] G. Bianconi, Phys. Rev. E, 2002, 66: 056123

[8] S. Lawrence and C. L. Giles, Nature (London), 1999, 400: 107

[9] D. J. Watts and S. H. Strogatz, Nature (London), 1998, 393: 440

[10] R. Albert, H. Jeong, and A. -L. Baraási, Nature (London), 1999, 401: 130

[11] L. A. Adamic and B. A. Huberman, Science, 2000, 287: 2115

[12] S. H. Strongatz, Nature, 2001, 410: 268

[13] C. Song, S. Havlin, and H. A. Makse, Nature, 2005, 433: 392

[14] H. P. Breuer, The Theory of Quantum Open Systems, New York: Oxford University Press, 2002

[15] Bi Qiao, X. S. Xing, and H. E. Ruda, Physica A, 2005, 355: 319

[16] M. Ohya and D. Petz, Quantum Entropy and Its Use, Berlin, Heidelberg: Springer-Verlag, 2004

[17] H. J. Carmichael, Statistical Methods in Quantum Optics 1, Master Equations and Fokker-Planck Equations, Berlin, Heidelberg: Springer-Verlag, 1999

[18] C. Arndt, Information Measures, Information and Its Description in Science and Engineering, Berlin, Heidelberg: Springer-Verlag, 2001

[19] X. S. Xing, On Dynamical statistical Information Theory, Transactions of Beijing Institute of Technology, 2004, 24: 1 (in Chinese); arXiv: cond-mat/0505009

[20] J. Q. Fang and Y. Liang, Chin. Phys. Lett., 2005, 22: 2719

[21] J. Q. Fang, Q. Bi, and Y. Liang, Front. Phys. China, 2007, 1: 109

[22] I. Stewart, IEEE Transactions on Circuits and Systems, CAS-30,1983: 578

[23] Q. Bi and H. E. Ruda, Physica A, 2003, 322:345

[24] I. Antoniou, Y. Melnikov, and Q. Bi, Physica A, 1997, 246: 97

[25] M. Catanzaro, G. Caldarelli, and L. Pietronero, Physica A, 2004, 338: 119

[26] M. E. J. Newman, Phys. Rev. Lett., 2002, 89: 208701

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Higher Education Press and Springer-Verlag Berlin Heidelberg