摘要
文章研究了由Uhlmann保真度诱导的高斯态量子相干度量CBu,通过sub-保真度,super-保真度以及Uhlmann保真度之间的关系,给出了单模与双模高斯纯态CBu的计算公式,并得到了单模与双模高斯混合态CBu的一个上下界。
We study the quantum coherence measure CBuof Gaussian states in terms of Uhlmann fidelity.The concrete formulas for 1-mode and 2-mode Gaussian pure states are given.In addition,an upper and lower bound of CBufor 1-mode and 2-mode Gaussian mixed states is also obtained.
引文
[1]Nielsen M A,Chuang I L.Quantum Computation And Quantum Information[M].Cambridge University Press,2001.
[2]Almeida J,Groot P C,Huelga S F,et al.Probing Quantum Coherence in Qubit Arrays[J].J Phys B,2013,46:104002.DOI:10.1088/0953-4075/46/10/104002.
[3]Lostaglio M,Korzekwa K,Jennings D,et al.Quantum Coherence,Time-Translation Symmetry,and Thermodynamics[J].Phys Rev X,2015,5:021001.DOI:10.1103/PhysRevX.5.021001.
[4]Baumgratz T,Cramer M,Plenio M B.Quantifying Coherence[J].Phys Rev Lett,2014,113:140401.DOI:10.1103/PhysRevLett.113.140401.
[5]Streltsov A,Adesso G,Plenio M B.Colloquium:Quantum Coherence as a Resource[J].Rev Mod Phys,2017,89:041003.DOI:10.1103/RevModPhys.89.041003.
[6]Kwon H,Park,C Y,Tan K C,et al.Coherence,Asymmetry,and Quantum Macroscopicity[J].Phys Rev A,2018,97:012326.DOI:10.1103/PhysRevA.97.012326.
[7]Styliaris G,Venuti L C,Zanardi P.Coherence-Generating Power of Quantum Dephasing Processes[J].Phys Rev A,2018,97:032304.DOI:10.1103/PhysRevA.97.032304.
[8]Giorda P,Allegra M.Coherence in Quantum Estimation[J].J Phys A Math Theor,2018,51:025302.DOI:10.1088/1751-8121/aa9808.
[9]Zanardi P,Venuti L C.Quantum Coherence Generating Power,Maximally Abelian Subalgebras,and Grassmannian Geometry[J].Journal of Mathematical Physics,2018,59:012203.DOI:10.1063/1.4997146.
[10]Xi Z J,Hu M L,Li Y M,et al.Entropic Cohering Power in Quantum Operations[J].Quantum Information Processing,2018,17:34.DOI:10.1007/s11128-017-1803-8.
[11]Zhang Y R,Shao L H,Li Y M,et al.Quantifying Coherence in Infinite-Dimensional Systems[J].Phys Rev A,2016,93:012334.DOI:10.1103/PhysRevA.93.012334.
[12]Weedbrook C,Pirandola S,Garcia-Patron R,et al.Gaussian Quantum Information[J].Rev Mod Phys,2012,84(2):621-669.DOI:10.1103/RevModPhys.84.621.
[13]Xu J W.Quantifying Coherence of Gaussian States[J].Phys Rev A,2016,93:032111.DOI:10.1103/PhysRevA.93.032111.
[14]Daniela B,Nocerino G,Giuseppe P,et al.Quantum Coherence of Gaussian States,arXiv,2016,1609.00913[quant-ph].
[15]Wang L,Hou J C,Qi X F.Fidelity and Entanglement Fidelity for Infinite-Dimensional Quantum Systems[J].J Phys AMath Theor,2014,47:335304.DOI:10.1088/1751-8113/47/33/335304.
[16]Qi X F,Wang L.Sub-Fidelity and Super-Fidelity Between Gaussian States[J].Communications in Theoretical Physics,2015,64:305-308.
[17]Miszczak J A,Puchala Z,Horodecki P,et al.Sub-and Super-Fidelity as Bounds for Quantum Fidelity[J].Quantum Inf Comput,2009,9:103-130.
[18]Marian P,Marian T A.Uhlmann Fidelity Between Two-Mode Gaussian States[J].Phys Rev A,2012,86:022340.DOI:10.1103/PhysRevA.86.022340.