Quantum multicast schemes of different quantum states via non-maximally entangled channels with multiparty involvement

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.

A Practical Quantum Network Coding Protocol Based on Non-Maximally Entangled State

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.

Probabilistic Teleportation of an Arbitrary Unknown Two-Qubit State via Positive Operator-Valued Measure and Two Non-maximally Entangled States

We present a scheme for probabilistically teleporting an arbitrary unknown two-qubit state through a quantum channel made up of two nonidentical non-maximally entangled states. In this scheme, the probabilistic teleportation is realized by using a proper positive operator-valued measure instead of usual projective measurement.

Probabilistic and Hierarchical Quantum Information Splitting Based on the Non-Maximally Entangled Cluster State

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.

Cooperative Communications via Dual-Teleportation with Non-maximally Entanglement Measurements

We investigate a framework of the cooperative quantum teleportation (CQT) based on non-maximally entangled state basis (NB) measurements,instead of maximally entangled state basis (MB) measurements.It is implemented with two consecutive conventional (or direct) quantum telportations (DQT),where unknown quantum states can be transmitted in a point-to-point fashion.The security is based on the quantum-mechanical impossibility of local unitary transformations between non-maximally entangled states.It shows that the CQT can enhance the successful transmissions by self-correcting the errors introduced in the dual-teleportations.

YAU'S UNIFORMIZATION CONJECTURE FOR MANIFOLDS WITH NON-MAXIMAL VOLUME GROWTH

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.

Controlled Secure Quantum Dialogue Using a Pure Entangled GHZ States

We present a controlled secure quantum dialogue protocol using a non-maximally （pure） entangled Greenberger-Horne-Zeibinger （GHZ） states at first, and then discuss the requirements for a real quantum dialogue. We show that the authorized two users can exchange their secret messages after purifying the non-maximally entangled GHZ states quantum channel unconditionally securely and simultaneously under the control of a third party.

Probabilistic teleportation of a non-symmetric three-particle state

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.

Universal quantum circuit evaluation on encrypted data using probabilistic quantum homomorphic encryption scheme

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.

Multiparty Quantum Secret Sharing via Introducing Auxiliary Particles Using a Pure Entangled State

We propose a new multiparty quantum secret sharing protocol via introducing auxiliary particles using a non-maximally entangled （pure） two-particle state without a Bell measurement. The communication parties utilize decoy particles tO check eavesdropping. After ensuring the security of the quantum channel, the sender encodes the secret message and transmits it to the receiver by using controlled-NOT operation and von Neumann measurement. If and only if all the agents agree to collaborate, they can read out the secret message.

Controlled Secure Quantum Communication Using Pure Entangled W Class States

We present a controlled secure quantum communication protocol using non-maximally （pure） entangled W states first, and then discuss the basic requirements for a real quantum communication. We show that the authorized two users can exchange their secret messages with the help of the controller after purifying the non-maximally entangled states quantum channel unconditionally securely and simultaneously. Our quantum communication protocol seems even more feasible within present technologies.

A generalized tripartite scheme for splitting an arbitrary 2-qubit state with three 2-qubit partially entangled states and the Kraus measurement

We put forward a generalized tripartite scheme for splitting an arbitrary 2-qubit pure state with three 2-qubit non-maximally en-tangled states as quantum channels.The scheme for the first time incorporates the Kraus measurement into quantum information splitting scheme.In contrast to the similar scheme using the same quantum channels and the ancilla-entangled measurement,our scheme is superior in terms of operation and complexity,success probability,resource consumption and effciency.