The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson ...In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.展开更多
The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. T...The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.展开更多
In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure f...In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.展开更多
We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterizati...We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions.展开更多
In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 ...In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 A and the set of regular quadratic forms, where A is a finite and a-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup (Tt)t∈R+ C L(l2 A) is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L(l2 A) is the yon Neumann algebra of all adjointable module maps on l2 A.展开更多
We give a simpler proof of a result on operator-valued Fourier multipliers on Lp([0, 2π]d; X) using an induction argument based on a known result when d= 1.
We propose a novel scheme to probabilistically transmit an arbitrary unknown two-qubit quantum state via Positive Operator-Valued Measurement with the help of two partially entangled states. In this scheme, the telepo...We propose a novel scheme to probabilistically transmit an arbitrary unknown two-qubit quantum state via Positive Operator-Valued Measurement with the help of two partially entangled states. In this scheme, the teleportation with two senders and two receives can be realized when the information of non-maximally entangled states is only available for the senders. Furthermore, the concrete implementation processes of this proposal are presented, meanwhile the classical communication cost and the successful probability of our scheme are calculated.展开更多
In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with ...In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such展开更多
A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X) state is presented in this paper. In the scheme, the send...A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X) state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice's secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.展开更多
Utilizing the generalized measurement described by positive operator-wlued measure, this paper comes up with a protocol for teleportation of an unknown multi-particle entangled (GHZ) state with a certain probability...Utilizing the generalized measurement described by positive operator-wlued measure, this paper comes up with a protocol for teleportation of an unknown multi-particle entangled (GHZ) state with a certain probability. The feature of the present protocol is to weaken requirement for the quantum channel initially shared by sender and receiver. All unitary transformations performed by receiver are summarized into a formula. On the other hand, this paper explicitly constructs the efficient quantum circuits for implementing the proposed teleportation by means of universal quantum logic operations in quantum computation.展开更多
We firstly present a novel scheme for deterministic joint remote state preparation of an arbitrary five-qubit Brown state using four Greenberg-Horme-Zeilinger (GHZ) entangled states as the quantum channel. The succe...We firstly present a novel scheme for deterministic joint remote state preparation of an arbitrary five-qubit Brown state using four Greenberg-Horme-Zeilinger (GHZ) entangled states as the quantum channel. The success probability of this scheme is up to 1, which is superior to the existing ones. Moreover, the scheme is extended to the generalized case where three-qubit and four-qubit non-maximally entangled states are taken as the quantum channel. We simultaneously employ two common methods to reconstruct the desired state. By comparing these two methods, we draw a conclusion that the first is superior to the second-optimal positive operator-valued measure only taking into account the number of auxiliary particles and the success probability.展开更多
Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit stat...Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements,and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement(POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.展开更多
The weighted Sobolev-Lions type spaces W pl,γ(Ω; E0, E) = W pl,γ(Ω; E) ∩ Lp,γ (Ω; E0) are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capa...The weighted Sobolev-Lions type spaces W pl,γ(Ω; E0, E) = W pl,γ(Ω; E) ∩ Lp,γ (Ω; E0) are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ(; E0, E) is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ(Ω; E0, E) to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.展开更多
In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(...In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]展开更多
The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-v...The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.展开更多
The moments of operator-valued semicircular distribution are calculated and a new relation between random variables which is called semi-independence is introduced. The asymp- totically free matrix models of operator-...The moments of operator-valued semicircular distribution are calculated and a new relation between random variables which is called semi-independence is introduced. The asymp- totically free matrix models of operator-valued semicircular distribution are given and a method is found to determine the freeness of some semicircular variables.展开更多
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal...This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators D^α from this space to Eα-valued Lp,γ spaces is proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.展开更多
Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are tw...Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are two Banach spaces and E 0 E.The most regular class of interpolation space E α,between E 0 and E are found such that the mixed differential operator D α is bounded and compact from B p,q l,s (Ω;E 0,E) to B p,q s (Ω;E α) and Ehrling-Nirenberg-Gagliardo type sharp estimates established.By using these results the separability of differential operators with variable coefficients and the maximal B-regularity of parabolic Cauchy problem are obtained.In applications,the infinite systems of the elliptic partial differential equations and parabolic Cauchy problems are studied.展开更多
文摘The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
基金Supported by National Natural Science Foundation of China(11471084,11301101,11971125)Young Innovative Talent Project of Department of Edcucation of Guangdong Province(2017KQNCX220)the Natural Research Project of Zhaoqing University(221622).
文摘In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.
文摘The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.
文摘In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.
基金The first author is supported by the NSF of China the Excellent Young Teachers Program of MOE,P.R.C.
文摘We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions.
基金supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.10XNJ033,"Study of Dirichlet forms and quantum Markov semigroups based on Hilbert C-modules")
文摘In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 A and the set of regular quadratic forms, where A is a finite and a-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup (Tt)t∈R+ C L(l2 A) is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L(l2 A) is the yon Neumann algebra of all adjointable module maps on l2 A.
基金supported by"Maximal Regularity for Vector-valued Boundary Problems"from the National Natural Science Foundation of China(Grant No.10571099)Specialized Research Fund for the Doctoral Program of Higher Education and the Tsinghua Basic Research Foundation(Grant No.JCpy2005056).
文摘We give a simpler proof of a result on operator-valued Fourier multipliers on Lp([0, 2π]d; X) using an induction argument based on a known result when d= 1.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60974037,61134008,11074307,and 61273202
文摘We propose a novel scheme to probabilistically transmit an arbitrary unknown two-qubit quantum state via Positive Operator-Valued Measurement with the help of two partially entangled states. In this scheme, the teleportation with two senders and two receives can be realized when the information of non-maximally entangled states is only available for the senders. Furthermore, the concrete implementation processes of this proposal are presented, meanwhile the classical communication cost and the successful probability of our scheme are calculated.
文摘In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such
基金Project supported by the National Natural Science Foundation of China (Grant No. 11071178) and the Research Foundation of the Education Department of Sichuan Province, China (Grant No. 12ZB106).
文摘A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X) state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice's secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.
基金Project supported by the National High Technology Research and Development Program of China(Grant No2006AA01Z419)the Major Research Plan of the National Natural Foundation of China(Grant No90604023)+1 种基金the National Laboratory for Modern Communications Science Foundation of China(Grant No9140C1101010601)the Natural Science Foundation of Beijing(Grant No4072020)
文摘Utilizing the generalized measurement described by positive operator-wlued measure, this paper comes up with a protocol for teleportation of an unknown multi-particle entangled (GHZ) state with a certain probability. The feature of the present protocol is to weaken requirement for the quantum channel initially shared by sender and receiver. All unitary transformations performed by receiver are summarized into a formula. On the other hand, this paper explicitly constructs the efficient quantum circuits for implementing the proposed teleportation by means of universal quantum logic operations in quantum computation.
基金supported by the National Natural Science Foundation of China(Grant Nos.61370194 and 61202082)the Fundamental Research Funds for the Central Universities of China(Grant Nos.BUPT2012RC0219)the Foundation of Science and Technology of Huawei of China
文摘We firstly present a novel scheme for deterministic joint remote state preparation of an arbitrary five-qubit Brown state using four Greenberg-Horme-Zeilinger (GHZ) entangled states as the quantum channel. The success probability of this scheme is up to 1, which is superior to the existing ones. Moreover, the scheme is extended to the generalized case where three-qubit and four-qubit non-maximally entangled states are taken as the quantum channel. We simultaneously employ two common methods to reconstruct the desired state. By comparing these two methods, we draw a conclusion that the first is superior to the second-optimal positive operator-valued measure only taking into account the number of auxiliary particles and the success probability.
基金Project supported by the National Natural Science Foundation of China(Grant No.61671087)
文摘Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements,and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement(POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.
文摘The weighted Sobolev-Lions type spaces W pl,γ(Ω; E0, E) = W pl,γ(Ω; E) ∩ Lp,γ (Ω; E0) are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ(; E0, E) is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ(Ω; E0, E) to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.
文摘In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]
文摘The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.
基金the National Natural Science Foundation of China (No.10771101)
文摘The moments of operator-valued semicircular distribution are calculated and a new relation between random variables which is called semi-independence is introduced. The asymp- totically free matrix models of operator-valued semicircular distribution are given and a method is found to determine the freeness of some semicircular variables.
基金This work is supported by the grant of Istanbul University (Project UDP-227/18022004)
文摘This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators D^α from this space to Eα-valued Lp,γ spaces is proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.
文摘Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are two Banach spaces and E 0 E.The most regular class of interpolation space E α,between E 0 and E are found such that the mixed differential operator D α is bounded and compact from B p,q l,s (Ω;E 0,E) to B p,q s (Ω;E α) and Ehrling-Nirenberg-Gagliardo type sharp estimates established.By using these results the separability of differential operators with variable coefficients and the maximal B-regularity of parabolic Cauchy problem are obtained.In applications,the infinite systems of the elliptic partial differential equations and parabolic Cauchy problems are studied.