Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state |n) → gn|n), with g being the amplification gain. We here gi...Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state |n) → gn|n), with g being the amplification gain. We here give a general frame- work for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0 1 photon subspace. In particular, we study if the local unitary is composed of sin- gle mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.展开更多
In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional produc...In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques.This protocol is initiated by the dealer Alice,who initially prepares a quantum product state,selected from a predefined set of orthogonal product states within the C~d■C~d framework.Subsequently,the participants execute unitary operations on this product state to recover the underlying secret.Furthermore,we subject the protocol to a rigorous security analysis,considering both eavesdropping attacks and potential dishonesty from the participants.Finally,we conduct a comparative analysis of our protocol against existing schemes.Our scheme exhibits economies of scale by exclusively employing quantum product states,thereby realizing significant cost-efficiency advantages.In terms of access structure,we adopt a(t, n)-threshold architecture,a strategic choice that augments the protocol's practicality and suitability for diverse applications.Furthermore,our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.展开更多
Any unknown unitary operations conditioned on a control system can be deterministically performed if ancillary subspaces are available for the target systems [Zhou X Q, et al. 2011 Nat. Commun. 2 413]. In this paper, ...Any unknown unitary operations conditioned on a control system can be deterministically performed if ancillary subspaces are available for the target systems [Zhou X Q, et al. 2011 Nat. Commun. 2 413]. In this paper, we show that previous optical schemes may be extended to general hybrid systems if unknown operations are provided by optical instruments. Moreover, a probabilistic scheme is proposed when the unknown operation may be performed on the subspaces of ancillary high-dimensional systems. Furthermore, the unknown operations conditioned on the multi-control system may be reduced to the case with a control system using additional linear circuit complexity. The new schemes may be more flexible for different systems or hybrid systems.展开更多
We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of trans...We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.展开更多
An efficient quantum secure direct communication network protocol with the two-step scheme is proposed by using the Einstein-Podolsky-Rosen (EPR) pair block as the quantum information carrier. The server, say Alice,...An efficient quantum secure direct communication network protocol with the two-step scheme is proposed by using the Einstein-Podolsky-Rosen (EPR) pair block as the quantum information carrier. The server, say Alice, prepares and measures the EPR pairs in the quantum communication and the users perform the four local unitary operations to encode their message. Anyone of the legitimate users can communicate another one on the network securely. Since almost all of the instances in this scheme are useful and each EPR pair can carry two bits of information, the efficiency for qubits and the source capacity both approach the maximal values.展开更多
In this paper a quantum dialogue scheme is proposed by using N batches of single photons. The same secret message is encoded on each batch of single photons by the sender with two different unitary operations, and the...In this paper a quantum dialogue scheme is proposed by using N batches of single photons. The same secret message is encoded on each batch of single photons by the sender with two different unitary operations, and then the N batches of single photons are sent to the receiver. After eavesdropping check, the message is encoded on the one remaining batch by the receiver. It is shown that the intercept-and-resend attack and coupling auxiliary modes attack can be resisted more efficiently, because the photons are sent only once in our quantum dialogue scheme.展开更多
An effcient multiparty quantum secret sharing scheme is proposed with Greenberger-Horne-Zeilinger (GHZ) states following some ideas in quantum dense coding. The agents take the single-photon measurements on the phot...An effcient multiparty quantum secret sharing scheme is proposed with Greenberger-Horne-Zeilinger (GHZ) states following some ideas in quantum dense coding. The agents take the single-photon measurements on the photons received for eavesdropping check and exploit the four local unitary operations Ⅰ, σx, σx and iσy to code their message. This scheme has the advantage of high capacity as each GHZ state can carry two bits of information. The parties do not need to announce the measuring bases for almost all the photons, which will reduce the classical information exchanged largely. The intrinsic efficiency for qubits and the total effciency both approach the maximal values.展开更多
A multiparty quantum secret report scheme is proposed with quantum encryption. The boss Alice and her M agents first share a sequence of (M + 1)-particle Greenberger-Horne-Zeilinger (GHZ) states that only Alice k...A multiparty quantum secret report scheme is proposed with quantum encryption. The boss Alice and her M agents first share a sequence of (M + 1)-particle Greenberger-Horne-Zeilinger (GHZ) states that only Alice knows which state each (M + 1)-particle quantum system is in. Each agent exploits a controlled-not (CNot) gate to encrypt the travelling particle by using the particle in the GHZ state as the control qubit. The boss Alice decrypts the travelling particle with a CNot gate after performing a aσ∞ operation on her particle in the GHZ state or not. After the GHZ states (the quantum key) are used up, the parties check whether there is a vicious eavesdropper, say Eve, monitoring the quantum line, by picking out some samples from the GHZ states shared and measuring them with two measuring bases. After confirming the security of the quantum key, they use the remaining GHZ states repeatedly for the next round of quantum communication. This scheme has the advantage of high intrinsic efficiency for the qubits and total efficiency.展开更多
By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional...By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation(FrST) which satisfies additivity.By virtue of the integration technique within the ordered product of operators(IWOP) we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa+a/2 and exp[iα/2(a^2 +a^+2).The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.展开更多
It has been found that for a fixed degree of fuzziness in the coarsened references of measurements,the quantum-toclassical transition can be observed independent of the macroscopicity of the quantum state.We explore a...It has been found that for a fixed degree of fuzziness in the coarsened references of measurements,the quantum-toclassical transition can be observed independent of the macroscopicity of the quantum state.We explore a general situation that the degree of fuzziness can change with the rotation angle between two states(different rotation angles represent different references).The fuzziness of reference comes from two kinds of fuzziness:the Hamiltonian(rotation frequency)and the timing(rotation time).For the fuzziness of the Hamiltonian alone,the degree of fuzziness for the reference will change with the rotation angle between two states,and the quantum effects can still be observed with any degree of fuzziness of Hamiltonian.For the fuzziness of timing,the degree of the coarsening reference is unchanged with the rotation angle.During the rotation of the measurement axis,the decoherence environment can also help the classical-to-quantum transition due to changing the direction of the measurement axis.展开更多
The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of the no-core Monte Carlo shell model (MCSM) calculations for ^3H...The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of the no-core Monte Carlo shell model (MCSM) calculations for ^3H and ^4He. The treatment of spurious center-of-mass motion by Lawson's prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson's prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations (NCSM). These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.展开更多
The nuclear system is a promising area for demonstrating practical quantum advantage.A comprehensive computation of a nuclear system in a classical computer is beyond the capacity of current classical computers.With t...The nuclear system is a promising area for demonstrating practical quantum advantage.A comprehensive computation of a nuclear system in a classical computer is beyond the capacity of current classical computers.With the rapid development of hardware,the prospect of using quantum computers in nuclear physics is close at hand.In this paper,we report a full quantum package,QCSH,for solving a nuclear shell model in a quantum computer.QCSH uses the linear combination of the unitary formalism of quantum computing and performs all calculations in a quantum computer.The complexities of qubit resource and the number of basic gates of QCSH are both polynomials to the number of nucleons in nuclei.For example,QCSH is used to calculate the binding energies of 12 light nuclei(i.e.,^(2)H,^(3)H,^(3)He,^(4)He,^(6)Li,^(7)Li,^(12)C,^(14)N,^(16)O,^(17)O,^(23)Na,and^(40)Ca).Moreover,we experimentally demonstrate the calculation of deuteron binding energy using a superconducting quantum processor.The result indicates that QCSH can provide meaningful results already in near-term quantum devices.展开更多
The most general duality gates were introduced by Long,Liu and Wang and named allowable generalized quantum gates (AGQGs,for short).By definition,an allowable generalized quantum gate has the form of U=YfkjsckUK,where...The most general duality gates were introduced by Long,Liu and Wang and named allowable generalized quantum gates (AGQGs,for short).By definition,an allowable generalized quantum gate has the form of U=YfkjsckUK,where Uk's are unitary operators on a Hilbert space H and the coefficients ck's are complex numbers with |Yfijo ck\ ∧ 1 an d 1ck| <1 for all k=0,1,...,d-1.In this paper,we prove that an AGQG U=YfkZo ck∧k is realizable,i.e.there are two d by d unitary matrices W and V such that ck=W0kVk0 (0<k<d-1) if and only if YfkJt 1c*|<m that case,the matrices W and V are constructed.展开更多
We develop subordinacy theory for extended Cantero-Moral-Velázquez(CMV) matrices,i.e.,we provide explicit supports for the singular and absolutely continuous parts of the canonical spectral measure associated wit...We develop subordinacy theory for extended Cantero-Moral-Velázquez(CMV) matrices,i.e.,we provide explicit supports for the singular and absolutely continuous parts of the canonical spectral measure associated with a given extended CMV matrix in terms of the presence or absence of subordinate solutions to the generalized eigenvalue equation.Some corollaries and applications of this result are described as well.展开更多
In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a un...In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).展开更多
We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the g...We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11304013,11204197,11204379 and 11074244the National Basic Research Program of China under Grant No 2011CBA00200+1 种基金the Doctor Science Research Foundation of Ministry of Education of China under Grant No 20113402110059Civil Aerospace 2013669
文摘Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state |n) → gn|n), with g being the amplification gain. We here give a general frame- work for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0 1 photon subspace. In particular, we study if the local unitary is composed of sin- gle mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.
基金supported by the National Natural Science Foundation of China(Grant No.12301590)the Natural Science Foundation of Hebei Province(Grant No.A2022210002)。
文摘In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques.This protocol is initiated by the dealer Alice,who initially prepares a quantum product state,selected from a predefined set of orthogonal product states within the C~d■C~d framework.Subsequently,the participants execute unitary operations on this product state to recover the underlying secret.Furthermore,we subject the protocol to a rigorous security analysis,considering both eavesdropping attacks and potential dishonesty from the participants.Finally,we conduct a comparative analysis of our protocol against existing schemes.Our scheme exhibits economies of scale by exclusively employing quantum product states,thereby realizing significant cost-efficiency advantages.In terms of access structure,we adopt a(t, n)-threshold architecture,a strategic choice that augments the protocol's practicality and suitability for diverse applications.Furthermore,our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61303039 and 61201253)Chunying Fellowship,and Fundamental Research Funds for the Central Universities,China(Grant No.2682014CX095)
文摘Any unknown unitary operations conditioned on a control system can be deterministically performed if ancillary subspaces are available for the target systems [Zhou X Q, et al. 2011 Nat. Commun. 2 413]. In this paper, we show that previous optical schemes may be extended to general hybrid systems if unknown operations are provided by optical instruments. Moreover, a probabilistic scheme is proposed when the unknown operation may be performed on the subspaces of ancillary high-dimensional systems. Furthermore, the unknown operations conditioned on the multi-control system may be reduced to the case with a control system using additional linear circuit complexity. The new schemes may be more flexible for different systems or hybrid systems.
文摘We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10447106, 10435020, 10254002, A0325401 and 10374010, and Beijing Education Committee under Grant No XK100270454.
文摘An efficient quantum secure direct communication network protocol with the two-step scheme is proposed by using the Einstein-Podolsky-Rosen (EPR) pair block as the quantum information carrier. The server, say Alice, prepares and measures the EPR pairs in the quantum communication and the users perform the four local unitary operations to encode their message. Anyone of the legitimate users can communicate another one on the network securely. Since almost all of the instances in this scheme are useful and each EPR pair can carry two bits of information, the efficiency for qubits and the source capacity both approach the maximal values.
基金Project supported by the Science Foundation of Yanbian University of China (Grant No 2005-20).
文摘In this paper a quantum dialogue scheme is proposed by using N batches of single photons. The same secret message is encoded on each batch of single photons by the sender with two different unitary operations, and then the N batches of single photons are sent to the receiver. After eavesdropping check, the message is encoded on the one remaining batch by the receiver. It is shown that the intercept-and-resend attack and coupling auxiliary modes attack can be resisted more efficiently, because the photons are sent only once in our quantum dialogue scheme.
基金Supported by the National Natural Science Foundation of China under Grant No 10447106, and Beijing Education Committee under Grant No XK100270454.
文摘An effcient multiparty quantum secret sharing scheme is proposed with Greenberger-Horne-Zeilinger (GHZ) states following some ideas in quantum dense coding. The agents take the single-photon measurements on the photons received for eavesdropping check and exploit the four local unitary operations Ⅰ, σx, σx and iσy to code their message. This scheme has the advantage of high capacity as each GHZ state can carry two bits of information. The parties do not need to announce the measuring bases for almost all the photons, which will reduce the classical information exchanged largely. The intrinsic efficiency for qubits and the total effciency both approach the maximal values.
基金Supported by the National Natural Science Foundation of China under Grant No 10447106, and Beijing Education Committee under Grant No XK100270454.
文摘A multiparty quantum secret report scheme is proposed with quantum encryption. The boss Alice and her M agents first share a sequence of (M + 1)-particle Greenberger-Horne-Zeilinger (GHZ) states that only Alice knows which state each (M + 1)-particle quantum system is in. Each agent exploits a controlled-not (CNot) gate to encrypt the travelling particle by using the particle in the GHZ state as the control qubit. The boss Alice decrypts the travelling particle with a CNot gate after performing a aσ∞ operation on her particle in the GHZ state or not. After the GHZ states (the quantum key) are used up, the parties check whether there is a vicious eavesdropper, say Eve, monitoring the quantum line, by picking out some samples from the GHZ states shared and measuring them with two measuring bases. After confirming the security of the quantum key, they use the remaining GHZ states repeatedly for the next round of quantum communication. This scheme has the advantage of high intrinsic efficiency for the qubits and total efficiency.
基金supported by the National Natural Science Foundation of China(Grant No.11304126)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20130532)+2 种基金the Natural Science Fund for Colleges and Universities in Jiangsu Province,China(Grant No.13KJB140003)the Postdoctoral Science Foundation of China(Grant No.2013M541608)the Postdoctoral Science Foundation of Jiangsu Province,China(Grant No.1202012B)
文摘By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation(FrST) which satisfies additivity.By virtue of the integration technique within the ordered product of operators(IWOP) we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa+a/2 and exp[iα/2(a^2 +a^+2).The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.
基金Project supported by the National Natural Science Foundation of China(Grant No.11375168)
文摘It has been found that for a fixed degree of fuzziness in the coarsened references of measurements,the quantum-toclassical transition can be observed independent of the macroscopicity of the quantum state.We explore a general situation that the degree of fuzziness can change with the rotation angle between two states(different rotation angles represent different references).The fuzziness of reference comes from two kinds of fuzziness:the Hamiltonian(rotation frequency)and the timing(rotation time).For the fuzziness of the Hamiltonian alone,the degree of fuzziness for the reference will change with the rotation angle between two states,and the quantum effects can still be observed with any degree of fuzziness of Hamiltonian.For the fuzziness of timing,the degree of the coarsening reference is unchanged with the rotation angle.During the rotation of the measurement axis,the decoherence environment can also help the classical-to-quantum transition due to changing the direction of the measurement axis.
基金Supported by Fundamental Research Funds for the Central Universities(JUSRP1035)National Natural Science Foundation of China(11305077)
文摘The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of the no-core Monte Carlo shell model (MCSM) calculations for ^3H and ^4He. The treatment of spurious center-of-mass motion by Lawson's prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson's prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations (NCSM). These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.
基金the National Natural Science Foundation of China(Grant No.12005015)support from the National Natural Science Foundation of China(Grant Nos.11974205,and 11774197)+1 种基金the National Key Research and Development Program of China(Grant No.2017YFA0303700)the Key Research and Development Program of Guangdong Province(Grant No.2018B030325002)。
文摘The nuclear system is a promising area for demonstrating practical quantum advantage.A comprehensive computation of a nuclear system in a classical computer is beyond the capacity of current classical computers.With the rapid development of hardware,the prospect of using quantum computers in nuclear physics is close at hand.In this paper,we report a full quantum package,QCSH,for solving a nuclear shell model in a quantum computer.QCSH uses the linear combination of the unitary formalism of quantum computing and performs all calculations in a quantum computer.The complexities of qubit resource and the number of basic gates of QCSH are both polynomials to the number of nucleons in nuclei.For example,QCSH is used to calculate the binding energies of 12 light nuclei(i.e.,^(2)H,^(3)H,^(3)He,^(4)He,^(6)Li,^(7)Li,^(12)C,^(14)N,^(16)O,^(17)O,^(23)Na,and^(40)Ca).Moreover,we experimentally demonstrate the calculation of deuteron binding energy using a superconducting quantum processor.The result indicates that QCSH can provide meaningful results already in near-term quantum devices.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571113 and 10871224)the Natural Science Research Program of Shaanxi Province (Grant No. 2009JM1011)
文摘The most general duality gates were introduced by Long,Liu and Wang and named allowable generalized quantum gates (AGQGs,for short).By definition,an allowable generalized quantum gate has the form of U=YfkjsckUK,where Uk's are unitary operators on a Hilbert space H and the coefficients ck's are complex numbers with |Yfijo ck\ ∧ 1 an d 1ck| <1 for all k=0,1,...,d-1.In this paper,we prove that an AGQG U=YfkZo ck∧k is realizable,i.e.there are two d by d unitary matrices W and V such that ck=W0kVk0 (0<k<d-1) if and only if YfkJt 1c*|<m that case,the matrices W and V are constructed.
基金supported by the Fundamental Research Grant Scheme from the Malaysian Ministry of Education(Grant No.FRGS/1/2018/STG06/XMU/02/1)Xiamen University Malaysia Research Fund(Grant No.XMUMRF/2020-C5/IMAT/0011)+3 种基金supported by China Scholarship Council(Grant No.201906330008)National Natural Science Foundation of China(Grant No.11571327)supported by National Science Foundation of USA(Grant No.DMS-1700131)Alexander von Humboldt Foundation。
文摘We develop subordinacy theory for extended Cantero-Moral-Velázquez(CMV) matrices,i.e.,we provide explicit supports for the singular and absolutely continuous parts of the canonical spectral measure associated with a given extended CMV matrix in terms of the presence or absence of subordinate solutions to the generalized eigenvalue equation.Some corollaries and applications of this result are described as well.
基金Supported by NSF 10301004,NSF 10171098Yantai University PHD Foundation SX03B14
文摘In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).
文摘We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.