The well-known Yau's uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal ...The well-known Yau's uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed, by G. Liu in [23]. In the first part, we will give a survey on thc progress. In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number Cn1 is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that, under bounded curvature conditions, Cn1 is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on Kahler manifolds with minimal volume growth.展开更多
Due to the unavoidable interaction between the quantum channel and its ambient environment,it is difficult to generate and maintain the maximally entanglement.Thus,the research on multiparty information transmission v...Due to the unavoidable interaction between the quantum channel and its ambient environment,it is difficult to generate and maintain the maximally entanglement.Thus,the research on multiparty information transmission via non-maximally entangled channels is of academic value and general application.Here,we utilize the non-maximally entangled channels to implement two multiparty remote state preparation schemes for transmitting different quantum information from one sender to two receivers synchronously.The first scheme is adopted to transmit two different four-qubit cluster-type entangled states to two receivers with a certain probability.In order to improve success probabilities of such multicast remote state preparation using non-maximally entangled channels,we put forward the second scheme,which deals with the situation that is a synchronous transfer of an arbitrary single-qubit state and an arbitrary two-qubit state from one sender to two receivers.In particular,its success probability can reach 100%in principle,and independent of the entanglement degree of the shared non-maximally entangled channel.Notably,in the second scheme,the auxiliary particle is not required.展开更多
In many earlier works,perfect quantum state transmission over the butterfly network can be achieved via quantum network coding protocols with the assist of maximally entangled states.However,in actual quantum networks...In many earlier works,perfect quantum state transmission over the butterfly network can be achieved via quantum network coding protocols with the assist of maximally entangled states.However,in actual quantum networks,a maximally entangled state as auxiliary resource is hard to be obtained or easily turned into a non-maximally entangled state subject to all kinds of environmental noises.Therefore,we propose a more practical quantum network coding scheme with the assist of non-maximally entangled states.In this paper,a practical quantum network coding protocol over grail network is proposed,in which the non-maximally entangled resource is assisted and even the desired quantum state can be perfectly transmitted.The achievable rate region,security and practicability of the proposed protocol are discussed and analyzed.This practical quantum network coding protocol proposed over the grail network can be regarded as a useful attempt to help move the theory of quantum network coding towards practicability.展开更多
With the emergence of classical communication security problems,quantum communication has been studied more extensively.In this paper,a novel probabilistic hierarchical quantum information splitting protocol is design...With the emergence of classical communication security problems,quantum communication has been studied more extensively.In this paper,a novel probabilistic hierarchical quantum information splitting protocol is designed by using a non-maximally entangled four-qubit cluster state.Firstly,the sender Alice splits and teleports an arbitrary one-qubit secret state invisibly to three remote agents Bob,Charlie,and David.One agent David is in high grade,the other two agents Bob and Charlie are in low grade.Secondly,the receiver in high grade needs the assistance of one agent in low grade,while the receiver in low grade needs the aid of all agents.While introducing an ancillary qubit,the receiver’s state can be inferred from the POVM measurement result of the ancillary qubit.Finally,with the help of other agents,the receiver can recover the secret state probabilistically by performing certain unitary operation on his own qubit.In addition,the security of the protocol under eavesdropping attacks is analyzed.In this proposed protocol,the agents need only single-qubit measurements to achieve probabilistic hierarchical quantum information splitting,which has appealing advantages in actual experiments.Such a probabilistic hierarchical quantum information splitting protocol hierarchical is expected to be more practical in multipartite quantum cryptography.展开更多
Homomorphic encryption has giant advantages in the protection of privacy information.In this paper,we present a new kind of probabilistic quantum homomorphic encryption scheme for the universal quantum circuit evaluat...Homomorphic encryption has giant advantages in the protection of privacy information.In this paper,we present a new kind of probabilistic quantum homomorphic encryption scheme for the universal quantum circuit evaluation.Firstly,the pre-shared non-maximally entangled states are utilized as auxiliary resources,which lower the requirements of the quantum channel,to correct the errors in non-Clifford gate evaluation.By using the set synthesized by Clifford gates and T gates,it is feasible to perform the arbitrary quantum computation on the encrypted data.Secondly,our scheme is different from the previous scheme described by the quantum homomorphic encryption algorithm.From the perspective of application,a two-party probabilistic quantum homomorphic encryption scheme is proposed.It is clear what the computation and operation that the client and the server need to perform respectively,as well as the permission to access the data.Finally,the security of probabilistic quantum homomorphic encryption scheme is analyzed in detail.It demonstrates that the scheme has favorable security in three aspects,including privacy data,evaluated data and encryption and decryption keys.展开更多
This paper proposes a scheme for teleporting a kind of essential three-particle non-symmetric entangled state, which is much more valuable than a GHZ and W state for some applications in quantum information processing...This paper proposes a scheme for teleporting a kind of essential three-particle non-symmetric entangled state, which is much more valuable than a GHZ and W state for some applications in quantum information processing. In comparison with previous proposal of teleportation, the resources of entangled states as quantum channel and the number of classical messages required by our scheme can be cut down. Moreover, it is shown that there exists a class of transformations which ensure the success of this scheme, because the two-particle transformation performed by the receiver in the course of teleportation may be a generic two-particle operation instead of a control-NOT (CNOT) operation. In addition, all kinds of transformations performed by sender and receiver are given in detail.展开更多
文摘The well-known Yau's uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed, by G. Liu in [23]. In the first part, we will give a survey on thc progress. In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number Cn1 is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that, under bounded curvature conditions, Cn1 is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on Kahler manifolds with minimal volume growth.
基金Project supported by the Key Industry Projects in Shaanxi Province,China(Grant Nos.2019ZDLGY09-03 and 2020ZDLGY15-09)the National Natural Science Foundation of China(Grant Nos.61771296,61372076,and 61301171)+1 种基金the Natural Science Foundation of Shaanxi Province,China(Grant Nos.2018JM60-53 and 2018JZ60-06)the 111 Project(Grant B08038).
文摘Due to the unavoidable interaction between the quantum channel and its ambient environment,it is difficult to generate and maintain the maximally entanglement.Thus,the research on multiparty information transmission via non-maximally entangled channels is of academic value and general application.Here,we utilize the non-maximally entangled channels to implement two multiparty remote state preparation schemes for transmitting different quantum information from one sender to two receivers synchronously.The first scheme is adopted to transmit two different four-qubit cluster-type entangled states to two receivers with a certain probability.In order to improve success probabilities of such multicast remote state preparation using non-maximally entangled channels,we put forward the second scheme,which deals with the situation that is a synchronous transfer of an arbitrary single-qubit state and an arbitrary two-qubit state from one sender to two receivers.In particular,its success probability can reach 100%in principle,and independent of the entanglement degree of the shared non-maximally entangled channel.Notably,in the second scheme,the auxiliary particle is not required.
基金supported by the National Natural Science Foundation of China(Grant Nos.61671087,92046001,61962009,61003287,61370188,61373131)the Scientific Research Common Program of Beijing Municipal Commission of Education(KM202010015009,KM201610015002)+6 种基金the Joint Funding Project of Beijing Municipal Commission of Education and Beijing Natural Science Fund Committee(KZ201710015010)the Initial Funding for the Doctoral Program of BIGC(27170120003/020)the Fok Ying Tung Education Foundation(Grant No.131067)the Fundamental Research Funds for the Central Universities(Grant No.2019XD-A02)the Fundamental Research Funds in Heilongjiang Provincial Universities(135509116)the Major Scientific and Technological Special Project of Guizhou Province(20183001)Huawei Technologies Co.Ltd.(No.YBN2020085019),PAPD and CICAEET funds.
文摘In many earlier works,perfect quantum state transmission over the butterfly network can be achieved via quantum network coding protocols with the assist of maximally entangled states.However,in actual quantum networks,a maximally entangled state as auxiliary resource is hard to be obtained or easily turned into a non-maximally entangled state subject to all kinds of environmental noises.Therefore,we propose a more practical quantum network coding scheme with the assist of non-maximally entangled states.In this paper,a practical quantum network coding protocol over grail network is proposed,in which the non-maximally entangled resource is assisted and even the desired quantum state can be perfectly transmitted.The achievable rate region,security and practicability of the proposed protocol are discussed and analyzed.This practical quantum network coding protocol proposed over the grail network can be regarded as a useful attempt to help move the theory of quantum network coding towards practicability.
基金This work is supported by the NSFC(Grant Nos.92046001,61571024,61671087,61962009,61971021)the Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data(Grant Nos.2018BDKFJJ018,2019BDKFJJ010,2019BDKFJJ014)+5 种基金the Open Research Project of the State Key Laboratory of Media Convergence and Communication,Communication University of China,China(Grant No.SKLMCC2020KF006)the High-quality and Cutting-edge Disciplines Construction Project for Universities in Beijing(Internet Information,Communication University of China)the Fundamental Research Funds for the Central Universities(Grant No.2019XD-A02)the Scientific Research Foundation of North China University of Technologythe Fundamental Research Funds for the Beijing Municipal Education CommissionJSPS KAKENHI Grant Number JP20F20080.
文摘With the emergence of classical communication security problems,quantum communication has been studied more extensively.In this paper,a novel probabilistic hierarchical quantum information splitting protocol is designed by using a non-maximally entangled four-qubit cluster state.Firstly,the sender Alice splits and teleports an arbitrary one-qubit secret state invisibly to three remote agents Bob,Charlie,and David.One agent David is in high grade,the other two agents Bob and Charlie are in low grade.Secondly,the receiver in high grade needs the assistance of one agent in low grade,while the receiver in low grade needs the aid of all agents.While introducing an ancillary qubit,the receiver’s state can be inferred from the POVM measurement result of the ancillary qubit.Finally,with the help of other agents,the receiver can recover the secret state probabilistically by performing certain unitary operation on his own qubit.In addition,the security of the protocol under eavesdropping attacks is analyzed.In this proposed protocol,the agents need only single-qubit measurements to achieve probabilistic hierarchical quantum information splitting,which has appealing advantages in actual experiments.Such a probabilistic hierarchical quantum information splitting protocol hierarchical is expected to be more practical in multipartite quantum cryptography.
基金the Fundamental Research Funds for the Central Universities(Grant No.2019XDA02)the Scientific Research Foundation of North China University of Technology。
文摘Homomorphic encryption has giant advantages in the protection of privacy information.In this paper,we present a new kind of probabilistic quantum homomorphic encryption scheme for the universal quantum circuit evaluation.Firstly,the pre-shared non-maximally entangled states are utilized as auxiliary resources,which lower the requirements of the quantum channel,to correct the errors in non-Clifford gate evaluation.By using the set synthesized by Clifford gates and T gates,it is feasible to perform the arbitrary quantum computation on the encrypted data.Secondly,our scheme is different from the previous scheme described by the quantum homomorphic encryption algorithm.From the perspective of application,a two-party probabilistic quantum homomorphic encryption scheme is proposed.It is clear what the computation and operation that the client and the server need to perform respectively,as well as the permission to access the data.Finally,the security of probabilistic quantum homomorphic encryption scheme is analyzed in detail.It demonstrates that the scheme has favorable security in three aspects,including privacy data,evaluated data and encryption and decryption keys.
基金Project supported by the National Natural Science Foundation of China (Grants No 60373059), the National Laboratory for Modern Communications Science Foundation of China (Grant No 51436020103DZ4001), the Major Research Plan of the National Natural Science Foundation of China (Grant No 90604023), the National Research Foundation for the Doctoral Program of Higher Education of China (Grant No 20040013007), and the ISN 0pen Foundation.
文摘This paper proposes a scheme for teleporting a kind of essential three-particle non-symmetric entangled state, which is much more valuable than a GHZ and W state for some applications in quantum information processing. In comparison with previous proposal of teleportation, the resources of entangled states as quantum channel and the number of classical messages required by our scheme can be cut down. Moreover, it is shown that there exists a class of transformations which ensure the success of this scheme, because the two-particle transformation performed by the receiver in the course of teleportation may be a generic two-particle operation instead of a control-NOT (CNOT) operation. In addition, all kinds of transformations performed by sender and receiver are given in detail.