两体懒态的几种刻画
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摘要
通过验证两体量子态算子矩阵表示中的算子元和约化态之间的交换关系,给出一个懒态判据.受非交换性度量的启发,引入一种懒态度量,此度量对应一个非负函数,任意给定的一个两体量子态是懒态当且仅当其对应的度量值为0.类似相对相干度量,定义下相对相干度量,利用它构造了相应的懒态判据.在无限维情形下,找到了一类可分但不是懒态的两体态;此外,研究了懒态和量子失协为0的态之间的关系.
By verifying the commutation relation between the elements of the operator matrix representation of a bipartite state and the corresponding reduced state,a lazy state criterion was given.Inspired by the non-commutativity measure,a lazy measure was introduced,which corresponded to a non-negative function,any given bipartite state was lazy if and only if the corresponding lazy measure was 0.Similar to the relative coherence measure,the sub-relative coherence measure was defined,and a corresponding lazy criterion in terms of sub-relative coherence measure was proposed.Under the infinite-dimensional setting,a class of separable but not lazy states was found;besides,the relation between the lazy states and the discordant states were investigated.
By verifying the commutation relation between the elements of the operator matrix representation of a bipartite state and the corresponding reduced state,a lazy state criterion was given.Inspired by the non-commutativity measure,a lazy measure was introduced,which corresponded to a non-negative function,any given bipartite state was lazy if and only if the corresponding lazy measure was 0.Similar to the relative coherence measure,the sub-relative coherence measure was defined,and a corresponding lazy criterion in terms of sub-relative coherence measure was proposed.Under the infinite-dimensional setting,a class of separable but not lazy states was found;besides,the relation between the lazy states and the discordant states were investigated.
引文
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[18]Baumgratz T,Cramer M,Plenio M B.Quantifying coherence[J].Physical Review Letters,2013,113(14):140401.
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[22]段周波.无限维系统上的信道、熵交换及相关问题研究[D].太原:太原理工大学,2017.
[2]Modi K.The classical-quantum boundary for correlations:discord and related measures[J].Reviews of Modern Physics,2012,84(4):1655-1707.
[3]Rodriguez-Rosario C A,Kimura G,Imai H,et al.Sufficient and necessary conditon for zero quantum entropy rates under any coupling to the environment[J].Physical Review Letters,2011,106(5):050403.
[4]Hulter A,Wehner S.Almost all quantum states have low entropy rates for any coupling to the enviroment[J].Physical Review Letters,2012,108(7):070501.
[5]Chruscinski L,Jurkowski J.Quantum damped oscillator I:dissipation and resonances[J].Annals of Physics,2006,321(4):854-874.
[6]Rulli C C,Sarandy M S.Global quantum discord in multipartite systems[J].Physical Review A,2011,84(4):5388-5393.
[7]Dong P C,Kim J S,Lee K.Generalized entropy and global quantum discord in multiparty quantum systems[J].Physical Review A,2013,87(6):944-948.
[8]Liu S Y,Zhang Y R,Zhao L M,et al.General monogamy property of global quantum discord and the application[J].Annals of Physics,2014,348(9):256-269.
[9]Chruscinski D,Jurkowski J,Kossakowski A.Quantum states with strong positive partial transpose[J].Physical Review A,2008,77(2):140-144.
[10]Ferraro A,Aolita L,Cavalcanti D,et al.Almost all quantum states have nonclassical correlations[J].Physical Review A,2010,81(81):90-96.
[11]Ferraro E,Messina A,Nikitin A G.Exactly solvable relativistic model with the anomalous interaction[J].Physical Review A,2010,81(4):82-90.
[12]Xu J W.Lazy states,discordant states and entangled states for 2-qubit systems[J].International Journal of Modern Physics B,2015,29(18):1550121.
[13]Xu J W.Which bipartite states are lazy[J].International Journal of Theoretical Physics,2015,54(3):860-867.
[14]Guo Y,Hou J C.Detecting quantum correlations by means of local noncommutativity[J].Mathematics,2012,arXiv:1107.0355v3.
[15]Guo Y.Non-commutativity measure of quantum discord[J].Scientific Reports,2016,6:25241.
[16]Ma T,Zhao M J,Wang Y K,et al.Non-commutativity and local indistinguish ability of quantum states[J].Scientific Reports,2014,4:6336.
[17]Chruscinski D,Jurkowski J,Kossakowski A.Quantum states with strong positive partial transpose[J].Physical Review A,2008,77(2):140-144.
[18]Baumgratz T,Cramer M,Plenio M B.Quantifying coherence[J].Physical Review Letters,2013,113(14):140401.
[19]Yuan X,Zhou H Y,Cao Z,et al.Intrinsic randomness as a measure of quantum coherence[J].Physical Review A,2015,92(2):022124.
[20]Hu M L,Fan H.Relative quantum coherence,incompatibility,and quantum correlations of states[J].Physical Review A,2017,95(5):052106.
[21]Guo Y,Hou J C.Comment on“Remarks on the structure of states of composite quantum systems and envariance”[J].Physics Letters A,2011,375(7):1160-1162.
[22]段周波.无限维系统上的信道、熵交换及相关问题研究[D].太原:太原理工大学,2017.