Abstract
The Kraus form of the completely positive dynamical maps is appealing from the mathematical and the point of the diverse applications of the open quantum systems theory. Unfortunately, the Kraus operators are poorly known for the two-qubit processes. In this paper, we derive the Kraus operators for a pair of interacting qubits, while the strength of the interaction is arbitrary. One of the qubits is subjected to the x-projection spin measurement. The obtained results are applied to calculate the dynamics of the entanglement in the qubits system. We obtain the loss of the correlations in the finite time interval; the stronger the inter-qubit interaction, the longer lasting entanglement in the system.
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References
K. Kraus. States, effects and operations, fundamental notions of quantum theory (Springer, Berlin, 1983)
H.P. Breuer, F. Petruccione. The theory of open quantum systems (Clarendon, Oxford, 2002)
Á. Rivas, S.F. Huelga. Open quantum systems—an introduction (Springer Briefs in Physics, Berlin, 2012)
J. Jeknić-Dugić, M. Arsenijević, M. Dugić, Proc. R. Soc. A. 470, 20140283 (2014)
J. Jeknić-Dugić, M. Arsenijević, M. Dugić, Proc. R. Soc. A. 472, 20160041 (2016)
L. Ferialdi, Phys. Rev. A. 95, 052109 (2017)
M.A. Nielsen, I.L. Chuang. Quantum computation and quantum information (Cambridge Univ Press, Cambridge, 2000)
M. Arsenijević, J. Jeknić-Dugić, M. Dugić, Braz. J. Phys. 47, 339349 (2017)
E. Andersson, J.D. Cresser, M.J.W. Hall, J. Mod. Opt. 54, 1695 (2007)
L.E. Ballentine, Rev, Phys. A. 43, 9 (1991)
B. Vacchini, Int. J. Theor. Phys. 44, 1011 (2005)
M.T. Mitchison, M.B. Plenio, New J. of Phys. 20, 033005 (2018)
P.P. Hofer, et al., New J. of Phys. 19, 123037 (2017)
J. Onam Gonzalez, et al., Open Sys. Inf. Dyn. 24, 1740010 (2017)
G.L. Deçordi, A. Vidiella-Barranco, Opt. Commun. 387, 366 (2017)
A.S. Trushechkin, I.V. Volovich, EPL. 113, 30005 (2016)
M. Arsenijević, J. Jeknić-Dugić, D. Todorović, M. Dugić, Vol. 2015. Entanglement relativity in the foundations of the open quantum systems theory, new research on quantum entanglement (Lori Watson, Nova Science Publishers, 2015), pp. 99–116
S.J. Yun, et al., J. Phys. B, At. Mol. Opt. Phys. 48, 075501 (2015)
B.M. Garraway, P.L. Knight, Phys. Rev. A. 54, 3592 (1996)
K.L. Viisanen, S.S. Simone Gasparinetti, O. Saira, J. Ankerhold, J.P. Pekola, New J. Phys. 17, 055014 (2015)
S. Hamedani Raja, M. Borrelli, R. Schmidt, J.P. Pekola, S. Maniscalco, Phys. Rev. A. 97, 032133 (2018). arXiv:1708.04458 [quant-ph]
Á. Rivas, A. Douglas, K. Plato, S.F. Huelga, M.B Plenio, New J. Phys. 12, 113032 (2010)
W.H. Louisell. Quantum statistical properties of radiation (Wiley, New York, 1973), p. 182
W.K. Wootters, Rev, Phys. Lett. 80, 2245 (1998)
T. Yu, J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004)
M. Arsenijević, J. Jeknić-Dugić, M. Dugić, Chin. Phys. B. 22, 020302 (2013)
R.E. Kastner, J. Jeknić-Dugić, G. Jaroszkiewicz (eds.), Quantum Structures. Classical Emergence from the Quantum Level (World Scientific, Singapore, 2017)
A. Brodutch, A. Datta, K. Modi, Á. Rivas, C.A. Rodríguez-Rosario, Phys. Rev. A. 87, 042301 (2013)
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Arsenijević, M., Jeknić-Dugić, J. & Dugić, M. Kraus Operators for a Pair of Interacting Qubits: a Case Study. Braz J Phys 48, 242–248 (2018). https://doi.org/10.1007/s13538-018-0570-z
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DOI: https://doi.org/10.1007/s13538-018-0570-z