一类基于k-体分划的多体态的量子关联测度A Class of Multipartity Quantum Correlation Measures Based on k-Partition
刘天文,王银珠
摘要(Abstract):
量子关联在量子信息任务中起着极其重要的作用,量化量子态的关联是其中最主要的问题之一。文章给出了一类基于k-体分划的多体量子态的量子关联测度,它可以量化多体态相对于k-体分划的非经典关联性,同时证明了其满足量子关联度的一些必要性质,包括局部酉操作下保持不变,局部量子操作下不增,凸性,连续性以及在添加局部非相干辅助子系统下的不变性。
关键词(KeyWords): 多体量子系统;k可分性;k-积态;量子关联度;迹距离
基金项目(Foundation):
作者(Author): 刘天文,王银珠
参考文献(References):
- [1] NIELSEN M A,CHUANG I L.Quantum Computatation and Quantum Information.Cambridge[M].UK:Cambridge University Press,2000.
- [2] EKERT A K.Quantum cryptography based on Bell's theorem[J].Phys Rev Lett,1991,67:661-663.
- [3] BENNETT C H,BRASSARD G,CREPEAU C,et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J].Phys Rev Lett,1993,70:1895-1899.
- [4] BENNETT C H,BRASSARD G,MERMIN N D.Quantum cryptography without Bell's theorem[J].Phys Rev Lett,1992,68:557-559.
- [5] GAO T,YAN F L,WANG Z X.Deterministic secure direct communication using GHZ states and swapping quantum entanglement[J].J Phys A:Math Gen,2005,38:5761.
- [6] BENNETT C H,DIVINCENZO D P.Quantum information and computation[J].Nature,2000,404:247-255.
- [7] 王建荣,赖云忠.色散对T-C模型两原子纠缠演化特征的影响[J].太原科技大学学报,2009,30(4):346-349.
- [8] 乔翠芳,杨旭东.四能级Tripod原子系统中相干增强的非线性效应[J].太原科技大学学报,2017,38(4):319-325.
- [9] HORODECKI R,HORODECKI P,HORODECKI M,et al Quantum entanglement[J].Rev Mod Phys,2009,81:865.
- [10] WERNER R F.Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden variable model[J].Phys.Rev.A,1989,40:4277-4281.
- [11] HORODECKI M,HORODECKI P,HORODECKI R.Separability of mixed states:Necessary and sufficient conditions[J].Phys Lett A,1996,223:1-14.
- [12] CHEN K,WU L A.A matrix realignment method for recognizing entanglement[J].Quant Inf Comput,2003,3:193-202.
- [13] NIELSEN M A,KEMPE J.Separable states are more disordered globally than locally[J].Phys Rev Lett,2001,86:5184-5187.
- [14] HORODECKI P.Separability criterion and inseparable mixed states with positive partial transposition[J].Phys Lett A,1997,232:333-339.
- [15] HOU J C.A characterization of positive linear maps and criteria of entanglement for quantum states[J].Journal of Physics A:Mathematical and Theoretical,2010,43,385201.
- [16] WANG Y Z,HOU J C,GUO Y.An entanglement criterion for states in infinite dimensional multipartite quantum systems[J].Chinese Science Bulletin.2012,57(14):1643-1647.
- [17] 王银珠,王旦霞.无限维多体复合量子系统态的算子不等式判据[J].数学的实践与认识,2018,48(23):227-231.
- [18] 王银珠,刘喜波.无限维多体复合量子系统态的约化判据[J].数学的实践与认识,2014,44(14)296-301.
- [19] GABRIEL A,HIESMAYR B C,HUBER M.Criterion for k-separability in mixed multipartite states[J].Quantum Information and Computation,2010,10:0829-0836.
- [20] GAO T,HONG Y.Detection of genuinely entangled and nonseparable n-partite quantum states[J].Phys Rev A,2010,82:062113.
- [21] WANG Y Z,HOU J C.Some necessary and sufficient conditions for k-seaprability of multipartite pure states[J].Quantum Information Processing,2015,14(10):3711-3722.
- [22] OLLIVIER H,ZUREK W H.Quantum Discord:A Measure of the Quantumness of Correlations[J].Phys Rev Lett,2001,88017901.
- [23] HENDERSON L,VEDRAL V.Classical,quantum and total correlations[J].J.Phys.A:Gen,Phys.,2001,34(35):6899-6905.
- [24] LUO S L,FU S S.Measurement-Induced Non-locality[J].Phys.Rev.Lett.2011,106120401.
- [25] OPPERNHEIM J,HORODECKI M,HORODECKI P,et al.Thermodynamical Approach to Quantifying Quantum Correlations[J].Phys.Rev.Lett.2002,89180402.
- [26] GUIFRE V,ROLF T.Robustness of entanglement[J].Phys.Rev.A,1999,59:141 .
- [27] KAVAN M,AHARON B,HUGO C,et al The classical-quantum boundary for correlations:discord and related measures[J].Rev.Mod.Phys,2012,841655-1707.
- [28] AKIRA S,ROBABEH R,MIKIO N.Nonclassical correlation in a multipartite quantum system:two measures and evaluation[J].Phys.Rev.A,2008,77052101 .
- [29] ANDRE L F,EFRAIN B,JESUS G L.Cumulative measure of correlation for multipartite quantum states[J].International Journal of Modern Physics B,2014,281450050.