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The validity of factorization law for the entanglement evolution of two qubits coupled to two independent non-Markovian channels is investigated. It is found that for some initial states, such as the Bell state and the maximally entangled mixed state, the entanglement can be characterized by the factorized entanglement when the effects of the channels are weak. For the general initial states, the factorized entanglement provides us with a good approximation to characterize the entanglement dynamics when the entanglement is large.
[1] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (1st Edn.) (Cambridge: Cambridge University Press) p353
[2] Bennett C H, DiVincenzo D P 2000 Nature 404 247
[3] Breuer H P, Petruccione F 2002 The Theory of Open Quantum Systems (1st Edn.) (Oxford: Oxford University Press) p219
[4] Yu T, Eberly J H 2006 Phys. Rev. Lett. 97 140403
[5] Dodd P J, Halliwell J J 2004 Phys. Rev. A 69 052105
[6] Zyczkowski K, Horodecki P, Horodecki M, Horodecki R 2001 Phys. Rev. A 65 012101
[7] Verstraete F, Dehaene J, De Moor B 2001 Phys. Rev. A 64 010101(R)
[8] Konrad T, Melo de F, Tiersch M, Kasztelan C, Aragao A, Buchleitner A 2008 Nat. Phys. 4 99
[9] Piilo J, Maniscalco S, Härkönen K, Suominen K A 2008 Phys. Rev. Lett. 100 180402
[10] Li Z G, Fei S M, Wang Z D, Liu W M 2009 Phys. Rev. A 79 024303
[11] Yu C S, Yi X X, Song H S 2008 Phys. Rev. A 78 062330
[12] Li J G, Zou J, Shao B 2010 Phys. Rev. A 82 042318
[13] Li J G, Zou J, Shao B 2011 Phys. Lett. A 375 2300
[14] Piilo J, Härkönen K, Maniscalco S, Suominen K A 2009 Phys. Rev. A 79 062112
[15] Breuer H P, Piilo J 2009 Europhys. Lett. 85 50004
[16] Maniscalco S, Petruccione F 2006 Phys. Rev. A 73 012111
[17] Bellomo B, Lo Franco R, Compagno G 2007 Phys. Rev. Lett. 99 160502
[18] Ban M 2009 Phys. Rev. A 80 032114
[19] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[20] Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[21] Ishizaka S, Hiroshima T 2000 Phys. Rev. A 62 022310
[22] Verstraete F, Audenaert K, De Moor B 2001 Phys. Rev. A 64 012316
[23] Wei T C, Nemoto K, Goldbart P M, Kwiat P G, Munro W J, Verstraete F 2003 Phys. Rev. A 67 022110
[24] Li S B 2007 Phys. Rev. A 75 054304
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[1] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (1st Edn.) (Cambridge: Cambridge University Press) p353
[2] Bennett C H, DiVincenzo D P 2000 Nature 404 247
[3] Breuer H P, Petruccione F 2002 The Theory of Open Quantum Systems (1st Edn.) (Oxford: Oxford University Press) p219
[4] Yu T, Eberly J H 2006 Phys. Rev. Lett. 97 140403
[5] Dodd P J, Halliwell J J 2004 Phys. Rev. A 69 052105
[6] Zyczkowski K, Horodecki P, Horodecki M, Horodecki R 2001 Phys. Rev. A 65 012101
[7] Verstraete F, Dehaene J, De Moor B 2001 Phys. Rev. A 64 010101(R)
[8] Konrad T, Melo de F, Tiersch M, Kasztelan C, Aragao A, Buchleitner A 2008 Nat. Phys. 4 99
[9] Piilo J, Maniscalco S, Härkönen K, Suominen K A 2008 Phys. Rev. Lett. 100 180402
[10] Li Z G, Fei S M, Wang Z D, Liu W M 2009 Phys. Rev. A 79 024303
[11] Yu C S, Yi X X, Song H S 2008 Phys. Rev. A 78 062330
[12] Li J G, Zou J, Shao B 2010 Phys. Rev. A 82 042318
[13] Li J G, Zou J, Shao B 2011 Phys. Lett. A 375 2300
[14] Piilo J, Härkönen K, Maniscalco S, Suominen K A 2009 Phys. Rev. A 79 062112
[15] Breuer H P, Piilo J 2009 Europhys. Lett. 85 50004
[16] Maniscalco S, Petruccione F 2006 Phys. Rev. A 73 012111
[17] Bellomo B, Lo Franco R, Compagno G 2007 Phys. Rev. Lett. 99 160502
[18] Ban M 2009 Phys. Rev. A 80 032114
[19] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[20] Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[21] Ishizaka S, Hiroshima T 2000 Phys. Rev. A 62 022310
[22] Verstraete F, Audenaert K, De Moor B 2001 Phys. Rev. A 64 012316
[23] Wei T C, Nemoto K, Goldbart P M, Kwiat P G, Munro W J, Verstraete F 2003 Phys. Rev. A 67 022110
[24] Li S B 2007 Phys. Rev. A 75 054304
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