SOT-不可分离Witness的比较
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摘要
在可分无限维复Hilbert张量积空间上,每个SOT-不可分离正算子都能用某个SOT-不可分离witness来检测。通过讨论不同SOT-不可分离Witness的比较问题,分别给出它们可以比较、等价、最优、能同时检测某SOT-不可分离正算子以及不能同时检测任何SOT-不可分离正算子的充分必要条件。
On a tensor product of separable complex Hilbert space,every SOT-inseparable positive operator can be detected by an SOT-inseparability witness.In this paper,the relations of different SOT-inseparability witnesses is discussed.The necessary and sufficient conditions are given for two witnesses to be comparable,to be equivalent,to be optimal,to detect some common SOT-inseparable positive operators,and to detect no common SOT-inseparable positive operators,respectively.
On a tensor product of separable complex Hilbert space,every SOT-inseparable positive operator can be detected by an SOT-inseparability witness.In this paper,the relations of different SOT-inseparability witnesses is discussed.The necessary and sufficient conditions are given for two witnesses to be comparable,to be equivalent,to be optimal,to detect some common SOT-inseparable positive operators,and to detect no common SOT-inseparable positive operators,respectively.
引文
[1]NIELSEN M A,CHUANG I L.Quantum computatation and quantum information[M].Cambridge:Cambridge University Press,2000.
[2]CLARISSE L,WOCJAN P.On independent permutation separability criteria[J].Quantum Inf Comput,2006,6(3):277-278.
[3]GHNE O.Characterizing entanglement via uncertainty relations[J].Phys Rev Lett,2004,92(11):117903.
[4]HORODECKI M,HORODECKI P,HORODECKI R.Separability of mixed states:necessary and sufficient conditions[J].Phys Rev A,1996,223(1):1-8.
[5]HORODECKI M,HORODECKI P,HORODECKI R.Inseparable two spin-density matrices can be distilled to a singlet form[J]Phys Lett A,1997,78(4):574-577.
[6]HORODECKI M,HORODECKI P.Reduction criterion of separability and limits for a class of distillation protocols[J].Phys Rev Lett,1999,59(6):4206-4216.
[7]PERES A.Separability criterion for density matrices[J].Phys Rev Lett,1996,77(8):1413-1415.
[8]WERNER R F.Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model[J].Phys Rev A,1989,40(8):4277-4281.
[9]HOU J C,QI X F.Constructing entanglement witnesses for infinite-dimensional systems[J].Phys Rev A,2010,81(6):062351.
[10]STRMER E.Separable states and positive maps[J].Journal of Functional Analysis,2008,254(8):2303-2312.
[11]QI X F,HOU J C.Positive finite rank elementary operators and characterizing entanglement of states[J].Journal of Phys A:Math Theor,2011,44(21):215305.
[12]HOU J C.A characterization of positive linear maps and criteria of entanglement for quantum states[J].Journal Phys A:Math Theor,2010,43:385201.
[13]HOU J C,CHAI J F.Constructing separable states in infinite-dimensional systems by operator matrices[J].International Journal of Theoretical Physics,2016,56(1):1-10.
[14]HOU J C,GUO Y.When different entanglement witnesses detect the same entangled states[J].Physical Review,2010,82(5):052301.
[15]侯晋川,崔建莲.算子代数上的线性映射引论[M].北京:科学出版社,2002.
[16]DOUGLAS R G.On majorization and range inclusion of operators in Hilbert space[J].Proc Amer Math Soc,1966,17(2):413-415.
[2]CLARISSE L,WOCJAN P.On independent permutation separability criteria[J].Quantum Inf Comput,2006,6(3):277-278.
[3]GHNE O.Characterizing entanglement via uncertainty relations[J].Phys Rev Lett,2004,92(11):117903.
[4]HORODECKI M,HORODECKI P,HORODECKI R.Separability of mixed states:necessary and sufficient conditions[J].Phys Rev A,1996,223(1):1-8.
[5]HORODECKI M,HORODECKI P,HORODECKI R.Inseparable two spin-density matrices can be distilled to a singlet form[J]Phys Lett A,1997,78(4):574-577.
[6]HORODECKI M,HORODECKI P.Reduction criterion of separability and limits for a class of distillation protocols[J].Phys Rev Lett,1999,59(6):4206-4216.
[7]PERES A.Separability criterion for density matrices[J].Phys Rev Lett,1996,77(8):1413-1415.
[8]WERNER R F.Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model[J].Phys Rev A,1989,40(8):4277-4281.
[9]HOU J C,QI X F.Constructing entanglement witnesses for infinite-dimensional systems[J].Phys Rev A,2010,81(6):062351.
[10]STRMER E.Separable states and positive maps[J].Journal of Functional Analysis,2008,254(8):2303-2312.
[11]QI X F,HOU J C.Positive finite rank elementary operators and characterizing entanglement of states[J].Journal of Phys A:Math Theor,2011,44(21):215305.
[12]HOU J C.A characterization of positive linear maps and criteria of entanglement for quantum states[J].Journal Phys A:Math Theor,2010,43:385201.
[13]HOU J C,CHAI J F.Constructing separable states in infinite-dimensional systems by operator matrices[J].International Journal of Theoretical Physics,2016,56(1):1-10.
[14]HOU J C,GUO Y.When different entanglement witnesses detect the same entangled states[J].Physical Review,2010,82(5):052301.
[15]侯晋川,崔建莲.算子代数上的线性映射引论[M].北京:科学出版社,2002.
[16]DOUGLAS R G.On majorization and range inclusion of operators in Hilbert space[J].Proc Amer Math Soc,1966,17(2):413-415.