Relative entropy of entanglement of two-qubit ’X’ states

Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on.     

Local Channels Preserving Maximal Entanglement or Schmidt Number

It is well know that entanglement is invariant under local unitary operations. In this paper we show that a local channel preserves maximal entanglement state (MES) or preserves pure states with Schmidt number r (r is an arbitrarily fixed integer) if and only if it is a local unitary operation. That is, the only local channel that leaves entanglement invariant is the local unitary operation.     

Simpler criterion and flexibility of operation complexity for perfectly teleporting arbitrary n-qubit state with 2n-qubit pure state

A criterion for whether a pure-state quantum channel consisting of 2n qubits averagely distributed between two nodes can be used for perfectly teleporting an arbitrary n-qubit state via Bell-state measurements is educed.Specifically,a matrix is composed of the coefficients of the known channel state and whether the matrix is unitary decides the criterion.As the criterion is apparently different from the usual standard entanglement criterion (USEC),its applicability is enlarged and verified by other measuring bases.Thorough analyses have further simplified the resultant criterion,so that a much simpler criterion than the USEC is conclusively obtained.Moreover,the flexibility of operation complexity between the non-unitary measurements and the unitary reconstructions is explicitly exhibited.     

Complete set of operational measures for the characterization of three-qubit entanglement

We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end, we derive a new decomposition for arbitrary three-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.     

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N strongly correlated random variables for all values of N (and not just for large N).     

Riemannian quantum circuit

Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we present the theory of a unitary matrix related to a finite number of zeros of the Riemann-zeta function. The equivalent quantum circuit and the calculation of the entanglement of a multipartite quantum state produced by the Riemannian quantum circuit are also shown.     

The fully entangled fraction as an inclusive measure of entanglement applications

Characterizing entanglement in all but the simplest case of a two qubit pure state is a hard problem, even understanding the relevant experimental quantities that are related to entanglement is difficult. It may not be necessary, however, to quantify the entanglement of a state in order to quantify the quantum information processing significance of a state. It is known that the fully entangled fraction has a direct relationship to the fidelity of teleportation maximized under the actions of local unitary operations. In the case of two qubits we point out that the fully entangled fraction can also be related to the fidelities, maximized under the actions of local unitary operations, of other important quantum information tasks such as dense coding, entanglement swapping and quantum cryptography in such a way as to provide an inclusive measure of these entanglement applications. For two qubit systems the fully entangled fraction has a simple known closed-form expression and we establish lower and upper bounds of this quantity with the concurrence. This approach is readily extendable to more complicated systems.     

Three-Party Quantum State Sharing of an Arbitrary Unknown Two-Qubit State Based on Entanglement Swapping and Bell-State Measurements

We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using a four-qubit cluster-class state and a Bell state as a quantum channel. With a quantum controlled phase gate （QCPG） operation and a local unitary operation, any one of the two agents has the access to reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information. As all quantum resource can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. Moreover, the present scheme is more feasible with present-day technique.     

Optimal Schemes for Quantum Teleportation of Ten-Qubit State

A teleportation protocol for certain class of ten-qubit state by utilizing an eight-qubit entangled state as a quantum channel has been proposed. In this paper, we present an optimal scheme for the teleportation of a ten-qubit state by using a stochastic local operation and classical communication(SLOCC) equivalent to four-qubit χ state as entanglement channel. Only von Neumann type measurement, controlled-not (CNOT) operations and appropriate unitary operations are needed in this scheme. Receiver Bob can reconstruct the initial state by introducing the appropriate unitary transformation and auxiliary particles.

     

Quantum Dialogue by Using Non-Symmetric Quantum Channel

A protocol for quantum dialogue is proposed to exchange directly the communicator＇s secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence coding, local collective unitary operations, and entanglement swapping. In this protocol, during the process of trans- mission of particles, the transmitted particles do not carry any secret messages and are transmitted only one time. The protocol has higher source capacity than protocols using symmetric two-dimensional states. The security is ensured by the unitary operations randomly performed on all checking groups before the particle sequence is transmitted and the application of entanglement swapping.     

Quantification of continuous variable entanglement with only two types of simple measurements

Here we propose an experimental set-up in which it is possible to obtain the entanglement of a two-mode Gaussian state, be it pure or mixed, using only simple linear optical measurement devices. After a proper unitary manipulation of the two-mode Gaussian state only number and purity measurements of just one of the modes suffice to give us a complete and exact knowledge of the state’s entanglement.     

Teleportation of N-Particle Entangled GHZ State via Entanglement Swapping

In this scheme, N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N-particle entangled GHZ state via entanglement swapping. In order to realize this teleportation, the sender Alice operates Bell-state measurement on particles belonging to herself. Then she informs the results to the receiver Bob through classical communication. According to the results, Bob operates corresponding transformation to reconstruct the initial state. The advantage of this scheme is that it needs only one common unitary matrix for Alice＇s different results, which has a more general meaning. As a special case, teleporting an unknown three-particle entangled GHZ state is proposed.     

Generation of the nonlocal quantum entanglement of three three-level particles by local operations

We propose a scheme to realize the nonlocal quantum entanglement of three three-level particles by using a three-particle entangled state of three levels as a quantum channel with the aid of some local unitary transformations. This scheme can be directly generalized to the nonlocal quantum entanglement of N three-level particles.     

一般WGHZ态和它的退纠缠与概率隐形传态

给出了一般纠缠的WGHZ态，然后利用所得一般WGHZ态导出了一般纠缠的不同的W态，得到了不同退纠缠的条件，一般WGHZ态取不同的复系数为零时，有不同的退纠缠，并可得到不同的W态和不同的一般的Bell基，以上对退纠缠的讨论结果与通常用密度矩阵的可分性得的退纠缠条件一致.通过构造一个5×5 对角投影变换矩阵,解决了使用一般纠缠量子信道并不再引入辅助态时，态畸变的恢复问题，并且这里的对角投影变换矩阵U_M也与以往文献的不同，而且还更直接，进而解决了不引入辅助态并使用一般纠缠信道纠缠的一般WGHZ态的概率隐形传态的问题,本文关于对角的投影变换矩阵U_M的变换方法等可以直接推广到任意一般纠缠信道的一般纠缠态的概率隐形传态. 关键词： 隐形传态 纠缠 W态 量子信道     

Quantum Remote Control of Unitary Operations on a Qubit of Pure Entangled States

We consider the remote implementation of an arbitrary unitary operation on one qubit of a pure two-qubit entangled state with 100% efficiency via entanglement swapping in detail, then directly generalize this protocol from two-qubit to N-qubit entangled states. The overall classical information and distributed entanglement cost required for this quantum remote control protocol is less than the bi-directional quantum state teleportation method.     

Operator Entanglement of Two-Qubit Joint Unitary Operations Revisited: Schmidt Number Approach

The operator entanglement of two-qubit joint unitary operations is revisited. The Schmidt number, an important attribute of a two-qubit unitary operation, may have connection with the entanglement measure of the unitary operator. We find that the entanglement measure of a two-qubit unitary operators is classified by the Schmidt number of the unitary operators. We also discuss the exact relation between the operator entanglement and the parameters of the unitary operator.     

用Greenberger-Horne-Zeilinger态作量子信道实现多点控制的远程单比特幺正变换

提出了一个用三粒子纠缠的GHZ态作为量子信道实现多点控制的远程单比特幺正变换的操纵方案.在该方案中,发送者Alice能“传送”一个幺正变换给远距离的接收者Bob,此幺正变换的结构分别由Alice和Bob决定.而Alice与Bob间的量子信道宽度,亦远程单比特幺正变换的成功操纵几率则由第三者Cindy控制.Cindy与Alice（Bob）间的经典通讯也由Cindy控制.     

Loss of entanglement after propagation in a quantum noisy channel modeled by a canonical unitary operation in two qubits

In this work, we analyze the loss of entanglement of bipartite states after propagation in a noisy channel modeled by the interaction between the bipartite state and the environment through a canonical unitary form of a two-qubit gate. An analytic expression for the entanglement loss is found.