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Non-Markovian dynamics and entanglement in quantum Brownian motion. (English) Zbl 1168.81359

Summary: Dynamical aspects of quantum Brownian motion in a low temperature environment are investigated. We give a systematic calculation of quantum entanglement among two Brownian oscillators without invoking Born-Markov approximation widely used for the study of open systems. Our approach is suitable to probe short time dynamics at cold temperatures where many experiments on quantum information processing are performed.

MSC:

81S25 Quantum stochastic calculus
81P68 Quantum computation
60J65 Brownian motion

References:

[1] R. Laflamme, E. Knill, C. Negrevergne, R. Martinez, S. Sinha, D. G. Cory, in Experimental Quantum Computation and Information, ed. by F. De Martini, C. Monroe. Proceeding of the International School of Physics Enrico Fermi (IOP press, Amsterdam, Netherlands, 2002)
[2] A. Andre, D. DeMille, J.M. Doyle, M.D. Lukin, S.E. Maxwell, P. Rabl, R.J. Schoelkopf, P. Zoller, quant-ph/0605201
[3] Nakajima S. (1958). Prog. Theor. Phys. 20: 948 · Zbl 0084.21505 · doi:10.1143/PTP.20.948
[4] Zwanzig R. (1961). Lect. Theor. Phys. 3: 106
[5] Feynman R.P. and Vernon F.L. (1963). Ann. Phys 24: 118 · doi:10.1016/0003-4916(63)90068-X
[6] Leggett A.J., Chakravarty S., Dorsey A.T., Fisher M.P.A., Garg A. and Zwerger W. (1987). Rev. Mod. Phys. 59: 1 · doi:10.1103/RevModPhys.59.1
[7] Weiss U. (1999). Quantum Dissipative Systems. World Scientific, Sigapore · Zbl 1137.81301
[8] Shiokawa K. and Kapral R. (2002). J. Chem. Phys. 117: 7852 · doi:10.1063/1.1509745
[9] Einstein A., Podolsky B. and Rosen N. (1935). Phys. Rev. 47: 777 · Zbl 0012.04201 · doi:10.1103/PhysRev.47.777
[10] Wheeler J.A. and Zurek W.H. (eds.) (1983). Quantum Theory and Measurement. Princeton University Press, Princeton
[11] Giulini D. et al. (eds.) (1996). Decoherence and the Appearance of the Classical World in Quantum Theory. Springer, Berlin · Zbl 0855.00003
[12] Nielsen M.A. and Chuang I.L. (2000). Quantum Computation and Quantum Information. Cambridge University Press, Cambridge · Zbl 1049.81015
[13] Peres A. (1996). Phys. Rev. Lett. 77: 1413 · Zbl 0947.81003 · doi:10.1103/PhysRevLett.77.1413
[14] Horodecki P. (1997). Phys. Lett. A 232: 333 · Zbl 1053.81504 · doi:10.1016/S0375-9601(97)00416-7
[15] Simon R. (2000). Phys. Rev. Lett. 63: 2726 · doi:10.1103/PhysRevLett.84.2726
[16] Vidal G. and Werner R.F. (2002). Phys. Rev. A 65: 032314–1 · doi:10.1103/PhysRevA.65.032314
[17] Giedke G., Wolf M.M., Krüger O., Werner R.F. and Cirac J.I. (2003). Phys. Rev. Lett. 91: 107901–1 · doi:10.1103/PhysRevLett.91.107901
[18] Furusawa A., Sorensen J.L., Braunstein S.L., Fuchs C.A., Kimble H.J. and Polzik E.S. (1998). Science 282: 706 · doi:10.1126/science.282.5389.706
[19] Grosshans F., Van Assche G., Wenger J., Brouri R., Cerf N.J. and Grangier P. (2003). Nature 421: 238 · doi:10.1038/nature01289
[20] Rajagopal A.K. and Rendell R.W. (2001). Phys. Rev. A 63: 022116 · doi:10.1103/PhysRevA.63.022116
[21] Dodd P.J. and Halliwell J.J. (2004). Phys. Rev. A 69: 052105 · doi:10.1103/PhysRevA.69.052105
[22] Devoret M.H. and Martinis J.M. (2004). Quant. Inform. Process. 3: 163 · Zbl 1075.68599 · doi:10.1007/s11128-004-3101-5
[23] A.O. Caldeira, A.J. Leggett, Physica A121, 587 (1983); V. Hakim, V. Ambegaokar, Phys. Rev. A 32, 423 (1985); F. Haake, R. Reibold, Phys. Rev. A 32, 2462 (1985); H. Grabert, P.Schramn, G.L. Ingold, Phys. Rep. 168, 115 (1988); W.G. Unruh, W.H. Zurek, Phys. Rev. D 40, 1071 (1989); B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)
[24] Shiokawa K. and Hu B.L. (2004). Phys. Rev. A 70: 062106 · doi:10.1103/PhysRevA.70.062106
[25] Mandel L. and Wolf E. (1995). Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge
[26] W.H. Luiselle, Quantum Statistical Properties of Radiation (Wiley, New York, 1990); D. Walls, G.J. Milburn, Quantum Optics (Springer, Berlin, 1995); H.J. Carmicheal, Statistical Methods in Quantum Optics (Springer, Berlin, 1999)
[27] Williamson J. (1936). Amer. J. Math. 58: 141 · Zbl 0013.28401 · doi:10.2307/2371062
[28] Simon R. and Mukunda N. (1994). B. Dutta, Phys. Rev. A 4947: 1567 · doi:10.1103/PhysRevA.49.1567
[29] Adesso G., Serafini A. and Illuminati F. (2004). Phys. Rev. A 70: 022318 · doi:10.1103/PhysRevA.70.022318
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