In(Phys Lett A,2002,297:4-8) an entanglement criterion for finite-dimensional bipartite systems is proposed:If ρ AB is a separable state,then Tr(ρA2) Tr(ρ2) and Tr(ρB2) Tr(ρ2).In the present paper this criterion ...In(Phys Lett A,2002,297:4-8) an entanglement criterion for finite-dimensional bipartite systems is proposed:If ρ AB is a separable state,then Tr(ρA2) Tr(ρ2) and Tr(ρB2) Tr(ρ2).In the present paper this criterion is extended to infinite-dimensional bipartite and multipartite systems.The reduction criterion presented in(Phys Rev A,1999,59:4206-4216) is also generalized to infinitedimensional case.Then it is shown that the former criterion is weaker than the later one.展开更多
The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable are generalized t...The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable are generalized to infinite-dimensional systems.展开更多
In terms of the relation between the state and its reduced states, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entangl...In terms of the relation between the state and its reduced states, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.展开更多
Let N and M be nests on Banach spaces X and Y over the real or complex field F, respectively, with the property that if M ∈ M such that M_ =M, then M is complemented in Y. Let AlgN and AlgM be the associated nest alg...Let N and M be nests on Banach spaces X and Y over the real or complex field F, respectively, with the property that if M ∈ M such that M_ =M, then M is complemented in Y. Let AlgN and AlgM be the associated nest algebras. Assume that Ф ： AlgN → AlgM is a bijective map. It is proved that, if dim X = ∞ and if there is a nontrivial element in N which is complemented in X, then Ф is Lie multiplicative （i.e. Ф（[A, B]） = [Ф（A）, Ф（B）] for all A, B ∈ AlgN） if and only if Ф has the form Ф（A） = TAT^-1 ＋ τ（A） for all A ∈ AlgAN or Ф（A） = -TA^＊T^-1 ＋ τ（A） for all A ∈ AlgN, where T is an invertible linear or conjugate linear operator and τ ： AlgN →FI is a map with τ（[A, B]） = 0 for all A, B ∈ AlgN. The Lie multiplicative maps are also characterized for the case dim X 〈 ∞.展开更多
Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ：B（H） →B（K） satisfies φ（AB^＋ ＋ B^＋A） = φ（A）φ（B）^＋ ＋ φ（B）^＋φ（A） for every pair A, B ∈ B（H） if and on...Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ：B（H） →B（K） satisfies φ（AB^＋ ＋ B^＋A） = φ（A）φ（B）^＋ ＋ φ（B）^＋φ（A） for every pair A, B ∈ B（H） if and only if either φ（A） = cUAU^＋ for all A or φ（A） = cUA^＋U^＋ for all A; φ satisfies φ（AB^＋A） = φ;（A）φ;（B）^＋φ;（A） for every pair A, B ∈ B（H） if and only if either φ（A） = UAV for all A or φ（A） = UA^＋V for all A, where At denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U^tU = c^-1I and V^＋V = cI for some nonzero real number c.展开更多
We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of ...We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of the fidelity of the finite-dimensional case to the infinite-dimensional case.These are somewhat different from those for the finite-dimensional case.展开更多
基金supported by the National Natural Science Foundation of China (11171249)the Natural Science Foundation of Shanxi Province (2011021002-2)
文摘In(Phys Lett A,2002,297:4-8) an entanglement criterion for finite-dimensional bipartite systems is proposed:If ρ AB is a separable state,then Tr(ρA2) Tr(ρ2) and Tr(ρB2) Tr(ρ2).In the present paper this criterion is extended to infinite-dimensional bipartite and multipartite systems.The reduction criterion presented in(Phys Rev A,1999,59:4206-4216) is also generalized to infinitedimensional case.Then it is shown that the former criterion is weaker than the later one.
基金supported by the National Natural Science Foundation of China (10771157 and 10871111)TianYuan Foundation of China (11026161)+1 种基金Research Fund of Shanxi for Returned Scholars (2007-38)Research Fund of Shanxi University
文摘The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable are generalized to infinite-dimensional systems.
基金supported by the National Natural Science Foundation of China (11171249, 11271217)Research Fund for the Doctoral Program of Higher Education of China (20101402110012)+1 种基金China Postdoctoral Science Foundation (2012M520603)Research Start-up Fund for Doctors of Shanxi Datong University (2011-B-01)
文摘In terms of the relation between the state and its reduced states, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.
基金supported by National Natural Science Foundation of China (Grant No. 10871111)Tian Yuan Foundation of China (Grant No. 11026161)Foundation of Shanxi University
文摘Let N and M be nests on Banach spaces X and Y over the real or complex field F, respectively, with the property that if M ∈ M such that M_ =M, then M is complemented in Y. Let AlgN and AlgM be the associated nest algebras. Assume that Ф ： AlgN → AlgM is a bijective map. It is proved that, if dim X = ∞ and if there is a nontrivial element in N which is complemented in X, then Ф is Lie multiplicative （i.e. Ф（[A, B]） = [Ф（A）, Ф（B）] for all A, B ∈ AlgN） if and only if Ф has the form Ф（A） = TAT^-1 ＋ τ（A） for all A ∈ AlgAN or Ф（A） = -TA^＊T^-1 ＋ τ（A） for all A ∈ AlgN, where T is an invertible linear or conjugate linear operator and τ ： AlgN →FI is a map with τ（[A, B]） = 0 for all A, B ∈ AlgN. The Lie multiplicative maps are also characterized for the case dim X 〈 ∞.
基金Project supported by the National Natural Science Foundation of China (No.10471082) the Shanxi Provincial Natural Science Foundation of China (No.20021005).
文摘Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ：B（H） →B（K） satisfies φ（AB^＋ ＋ B^＋A） = φ（A）φ（B）^＋ ＋ φ（B）^＋φ（A） for every pair A, B ∈ B（H） if and only if either φ（A） = cUAU^＋ for all A or φ（A） = cUA^＋U^＋ for all A; φ satisfies φ（AB^＋A） = φ;（A）φ;（B）^＋φ;（A） for every pair A, B ∈ B（H） if and only if either φ（A） = UAV for all A or φ（A） = UA^＋V for all A, where At denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U^tU = c^-1I and V^＋V = cI for some nonzero real number c.
基金supported by the National Natural Science Foundation of China(Grant Nos.11171249 and 11101250)the Youth Foundation of Shanxi Province(Grant No.2012021004)the Young Talents Plan for Shanxi University and a grant from the International Cooperation Program in Sciences and Technology of Shanxi(Grant No.2011081039)
文摘We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of the fidelity of the finite-dimensional case to the infinite-dimensional case.These are somewhat different from those for the finite-dimensional case.
