检索结果-南通市图书馆

Existence and construction of simultaneous cloning machines for mixed states

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2015年第4期58卷 11-15页

作者： guo zhihua CAO HuaiXin QU ShiXian College of Mathematics and Information Science Shaanxi Normal University College of Physics and Information Technology Shaanxi Normal University

It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state. In other words, there does not exist a quantum cloning machine that can clone all quantum states. However, it is possible to clone given quantum states under certain conditions, for instance, k distinct pure states ｜ψ1〉, ｜ψ2）,....,｜ψk） can be cloned simultaneously if and only if they are orthogonal. This paper discusses the existence and construction of simultaneous cloning machines for mixed states. It is proved that k distinct mixed states Pl,P2 Pk of the n-dimensional quantum system Cn can be cloned simultaneously, that is, there exists a quantum channel Ф on .Mn ⊙ Mn and a state ∑ in Mn, such that Ф（ρi ⊙∑） = ρi ⊙ ρi for all i, if and only if ρiρj = 0 （i ≠j）. Also, the constructing procedure of the desired simultaneous cloning machine is given.

关键词： simultaneous cloning machine quantum channel mixed state

An upper bound for the adiabatic approximation error

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2014年第2期57卷 218-224页

作者： WANG WenHua guo zhihua CAO HuaiXin College of Mathematics and Information Science Shaanxi Normal University

In this paper, we derive an upper bound for the adiabatic approximation error, which is the distance between the exact solution to a Schrodinger equation and the adiabatic approximation solution. As an application, we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a SchrOdinger equation.

关键词： upper bound error adiabatic approximation

Existence and construction of a quantum channel with given inputs and outputs

在线全文

学校读者我要写书评

暂无评论

Chinese Science Bulletin 2012年第33期57卷 4346-4350页

作者： guo zhihua CAO HuaiXin College of Mathematics and Information Science Shaanxi Normal UniversityXi'an 710062China

We derive that sufficient and necessary conditions for existence of a quantum channel φ and a generalized unitary operation ε sending Ai to Bi(1≤ i≤ k) for two given families {Ai}i=1k,{Bi}i=1k of matrices,*** an application,a sufficient and necessary condition for existence of a unitary duality quantum computer with given input-output states is obtained.

关键词：量子通道输出状态输入充分必要条件量子计算机

Adiabatic approximation in PT-symmetric quantum mechanics

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2014年第10期57卷 1835-1839页

作者： guo zhihua CAO HuaiXin LU Ling College of Mathematics and Information Science Shaanxi Normal University Section of Military Operation Research Xi'an Military Academy

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

关键词： PT-symmetry time evolution equation adiabatic approximation error estimation

Freezing imaginarity of quantum states based onℓ_(1)-norm

在线全文

学校读者我要写书评

暂无评论

Chinese Physics B 2024年第10期33卷 166-175页

作者： Shuo Han Bingke Zheng zhihua guo School of Mathematics and Statistics Shaanxi Normal UniversityXi’an 710119China

We discuss freezing of quantum imaginarity based onℓ_(1)-*** properties about a quantity of imaginarity based onℓ_(1)-norm are *** a qubit(2-dimensional)system,we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any ***,we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of N-qubit quantum states.

关键词： imaginarity freezing ℓ_(1)-norm real operation

Quantitative sufficient conditions for adiabatic approximation

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2013年第7期56卷 1401-1407页

作者： CAO HuaiXin guo zhihua CHEN ZhengLi WANG WenHu College of Mathematics and Information Science Shaanxi Normal University

Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）：（1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values Fn（t） for all t are always on the circle centered at 1 with radius 1; （2） If a quantum system S with a time-dependent Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values F,（t） for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.

关键词： quantitative condition adiabatic approximation uniformly slowly evolving 6-uniformly slowly evolving

Complex duality quantum computers acting on pure and mixed states

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2012年第12期55卷 2452-2462页

作者： CAO HuaiXin CHEN ZhengLi guo zhihua REN Fangguo College of Mathematics and Information Science Shaanxi Normal UniversityXi'an 710062China

The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex *** is proved that the divider and the combiner of a CDQC are an isometry and a contraction,*** is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states(matrix-states) are also ***,the loss of an input state passing through a CDQC is measured.

关键词： complex duality quantum computer divider combiner

Computable upper bounds for the adiabatic approximation errors

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2014年第11期57卷 2031-2038页

作者： YU BaoMin CAO HuaiXin guo zhihua WANG WenHua College of Mathematics and Information Science Weinan Normal University College of Mathematics and Information Science Shaanxi Normal University

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this *** the gap-condition that|Ek(s)-En(s)|λ>0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,*** an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.

关键词： adiabatic bounds Hamiltonian fidelity Hermitian dilated numerically exact initially coherent

Operational properties and matrix representations of quantum measures

在线全文

学校读者我要写书评

暂无评论

Chinese Science Bulletin 2011年第16期56卷 1671-1678页

作者： guo zhihua CAO HuaiXin CHEN ZhengLi YIN JunCheng College of Mathematics and Information Science Shaanxi Normal University Xi' an 710062 China

Denoted by M(A),QM(A)and SQM(A)the sets of all measures,quantum measures and subadditive quantum measures on a σ-algebra A,*** observe that these sets are all positive cones in the real vector space F(A)of all real-valued functions on A and prove that M(A)is a face of SQM(A).It is proved that the product of m grade-1 measures is a grade-m *** combining a matrix Mμto a quantum measureμon the power set An of an n-element set X,it is proved thatμν(resp. μ⊥ν)if and only if μν M M(resp.MμMv=0).Also,it is shown that two nontrivial measuresμandνare mutually absolutely continuous if and only ifμ·ν∈QM(An).Moreover,the matrices corresponding to quantum measures are characterized. Finally,convergence of a sequence of quantum measures on An is introduced and discussed;especially,the Vitali-Hahn-Saks theorem for quantum measures is proved.

关键词：矩阵表示量子定理证明性质业务质量管理向量空间实值函数