Dynamics of Quantum Coherence in Bell-Diagonal States under Markovian Channels
|
摘要
We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.
We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.
We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.
引文
[1]E.Bagan,J.A.Bergou,S.S.Cottrell,and M.Hillery,Phys.Rev.Lett.116(2016)160406.
[2]P.K.Jha,M.Mrejen,J.Kim,et al.,Phys.Rev.Lett.116(2016)165502.
[3]P.Kammerlander and J.Anders,Sci.Rep.6(2016)22174.
[4]V.Giovannetti,S.Lloyd,and L.Maccone,Science 306(2004)1330.
[5]R.Demkowicz-Dobrza′nski and L.Maccone,Phys.Rev.Lett.113(2014)250801.
[6]V.Giovannetti,S.Lloyd,and L.Maccone,Nat.Photonics5(2011)222.
[7]R.J.Glauber,Phys.Rev.131(1963)2766.
[8]E.C.G.Sudarshan,Phys.Rev.Lett.10(1963)277.
[9]L.Mandel and E.Wolf,Optical Coherence and Quantum Optics,Cambridge University Press,Cambridge(1995).
[10]J.?Aberg,Phys.Rev.Lett.113(2014)150402.
[11]V.Narasimhachar and G.Gour,Nat.Commun.6(2015)7689.
[12]P.′Cwikli′nski,M.Studzi′nski,M.Horodecki,and J.Oppenheim,Phys.Rev.Lett.115(2015)210403.
[13]M.Lostaglio,D.Jennings,and T.Rudolph,Nat.Commun.6(2015)6383.
[14]M.Lostaglio,K.Korzekwa,D.Jennings,and T.Rudolph,Phys.Rev.X 5(2015)021001.
[15]H.Vazquez,R.Skouta,S.Schneebeli,et al.,Nat.Nanotechnol.7(2012)663.
[16]O.Karlstr¨om,H.Linke,G.Karlstr¨om,and A.Wacker,Phys.Rev.B 84(2011)113415.
[17]A.Misra,U.Singh,S.Bhattacharya,and A.K.Pati,Phys.Rev.A 93(2016)052335.
[18]M.B.Plenio and S.F.Huelga,New J.Phys.10(2008)113019.
[19]P.Rebentrost,M.Mohseni,and A.Aspuru-Guzik,J.Phys.Chem.B 113(2009)9942.
[20]S.Lloyd,J.Phys.:Conf.Ser.302(2011)012037.
[21]C.M.Li,N.Lambert,Y.N.Chen,et al.,Sci.Rep.2(2012)885.
[22]S.F.Huelga and M.B.Plenio,Contemp.Phys.54(2013)181.
[23]F.Levi and F.Mintert,New J.Phys.16(2014)033007.
[24]T.Baumgratz,M.Cramer,and M.B.Plenio,Phys.Rev.Lett.113(2014)140401.
[25]L.H.Shao,Z.Xi,H.Fan,and Y.Li,Phys.Rev.A 91(2015)042120.
[26]A.E.Rastegin,Phys.Rev.A 93(2016)032136.
[27]E.Chitambar and G.Gour,Phys.Rev.A 94(2016)052336.
[28]J.Ma,B.Yadin,D.Girolami,et al.,Phys.Rev.Lett.116(2016)160407.
[29]C.Radhakrishnan,M.Parthasarathy,S.Jambulingam,and T.Byrnes,Phys.Rev.Lett.116(2016)150504.
[30]A.Streltsov,U.Singh,H.S.Dhar,Phys.Rev.Lett.115(2015)020403.
[31]Y.Yao,X.Xiao,L.Ge,and C.P.Sun,Phys.Rev.A 92(2015)022112.
[32]Z.Xi,Y.Li,and H.Fan,Sci.Rep.5(2015)10922.
[33]T.R.Bromley,M.Cianciaruso,and G.Adesso,Phys.Rev.Lett.114(2015)210401.
[34]X.D.Yu,D.J.Zhang,C.L.Liu,and D.M.Tong,Phys.Rev.A 93(2016)060303.
[35]A.Streltsov,G.Adesso,and M.B.Plenio,Rev.Mod.Phys.89(2017)041003.
[36]S.C.Wang,Z.W.Yu,W.J.Zhou,and X.B.Wang,Phys.Rev.A 89(2014)022318.
[37]I.A.Silva,A.M.Souza,T.R.Bromley,et al.,Phys.Rev.Lett.117(2016)160402.
[38]M.A.Nielsen,and I.L.Chuang,Quantum Computation and Quantum Information,Cambridge University Press,Cambridge(2000).
[39]Y.K.Wang,S.M.Fei,Z.X.Wang,et al.,Sci.Rep.10(2015)10727.
[2]P.K.Jha,M.Mrejen,J.Kim,et al.,Phys.Rev.Lett.116(2016)165502.
[3]P.Kammerlander and J.Anders,Sci.Rep.6(2016)22174.
[4]V.Giovannetti,S.Lloyd,and L.Maccone,Science 306(2004)1330.
[5]R.Demkowicz-Dobrza′nski and L.Maccone,Phys.Rev.Lett.113(2014)250801.
[6]V.Giovannetti,S.Lloyd,and L.Maccone,Nat.Photonics5(2011)222.
[7]R.J.Glauber,Phys.Rev.131(1963)2766.
[8]E.C.G.Sudarshan,Phys.Rev.Lett.10(1963)277.
[9]L.Mandel and E.Wolf,Optical Coherence and Quantum Optics,Cambridge University Press,Cambridge(1995).
[10]J.?Aberg,Phys.Rev.Lett.113(2014)150402.
[11]V.Narasimhachar and G.Gour,Nat.Commun.6(2015)7689.
[12]P.′Cwikli′nski,M.Studzi′nski,M.Horodecki,and J.Oppenheim,Phys.Rev.Lett.115(2015)210403.
[13]M.Lostaglio,D.Jennings,and T.Rudolph,Nat.Commun.6(2015)6383.
[14]M.Lostaglio,K.Korzekwa,D.Jennings,and T.Rudolph,Phys.Rev.X 5(2015)021001.
[15]H.Vazquez,R.Skouta,S.Schneebeli,et al.,Nat.Nanotechnol.7(2012)663.
[16]O.Karlstr¨om,H.Linke,G.Karlstr¨om,and A.Wacker,Phys.Rev.B 84(2011)113415.
[17]A.Misra,U.Singh,S.Bhattacharya,and A.K.Pati,Phys.Rev.A 93(2016)052335.
[18]M.B.Plenio and S.F.Huelga,New J.Phys.10(2008)113019.
[19]P.Rebentrost,M.Mohseni,and A.Aspuru-Guzik,J.Phys.Chem.B 113(2009)9942.
[20]S.Lloyd,J.Phys.:Conf.Ser.302(2011)012037.
[21]C.M.Li,N.Lambert,Y.N.Chen,et al.,Sci.Rep.2(2012)885.
[22]S.F.Huelga and M.B.Plenio,Contemp.Phys.54(2013)181.
[23]F.Levi and F.Mintert,New J.Phys.16(2014)033007.
[24]T.Baumgratz,M.Cramer,and M.B.Plenio,Phys.Rev.Lett.113(2014)140401.
[25]L.H.Shao,Z.Xi,H.Fan,and Y.Li,Phys.Rev.A 91(2015)042120.
[26]A.E.Rastegin,Phys.Rev.A 93(2016)032136.
[27]E.Chitambar and G.Gour,Phys.Rev.A 94(2016)052336.
[28]J.Ma,B.Yadin,D.Girolami,et al.,Phys.Rev.Lett.116(2016)160407.
[29]C.Radhakrishnan,M.Parthasarathy,S.Jambulingam,and T.Byrnes,Phys.Rev.Lett.116(2016)150504.
[30]A.Streltsov,U.Singh,H.S.Dhar,Phys.Rev.Lett.115(2015)020403.
[31]Y.Yao,X.Xiao,L.Ge,and C.P.Sun,Phys.Rev.A 92(2015)022112.
[32]Z.Xi,Y.Li,and H.Fan,Sci.Rep.5(2015)10922.
[33]T.R.Bromley,M.Cianciaruso,and G.Adesso,Phys.Rev.Lett.114(2015)210401.
[34]X.D.Yu,D.J.Zhang,C.L.Liu,and D.M.Tong,Phys.Rev.A 93(2016)060303.
[35]A.Streltsov,G.Adesso,and M.B.Plenio,Rev.Mod.Phys.89(2017)041003.
[36]S.C.Wang,Z.W.Yu,W.J.Zhou,and X.B.Wang,Phys.Rev.A 89(2014)022318.
[37]I.A.Silva,A.M.Souza,T.R.Bromley,et al.,Phys.Rev.Lett.117(2016)160402.
[38]M.A.Nielsen,and I.L.Chuang,Quantum Computation and Quantum Information,Cambridge University Press,Cambridge(2000).
[39]Y.K.Wang,S.M.Fei,Z.X.Wang,et al.,Sci.Rep.10(2015)10727.