Catalytic Coherence Transformation and Distillation for Special Mixed States

The coherence transformation and distillation for a class of special mixed coherent states of rank-2 under incoherent operations (IO) is discussed. Similar to the entanglement transformation for mixed entangled states, the catalytic coherence transformation for this class of special mixed coherent states is analyzed. On the one hand, it is found that some of the mixed coherent states can be converted into other mixed coherent states under IO. But for those mixed coherent states which fail in the coherence conversion under IO, the catalytic coherence manipulation can solve this problem. In this case, a mixed coherent state cannot be converted into another under IO, while the coherence transformation can be realized with the help of coherence-assisted incoherent operations, that is, catalytic coherence transformation. On the other hand, these special mixed coherent states can be distilled into the maximally pure coherent states or mixed states of arbitrary dimensions by strictly incoherent operations with certain probabilities. Finally, the coherence transformation of this type of mixed states can be generalized to the case of higher rank in a similar way, which is discussed at the end of this paper.     

Multiparty Quantum Secret Sharing of Quantum States Using Entanglement States

A multi-partite-controlled quantum secret sharing scheme using several non-orthogonal entanglement states is presented with unconditional security. In this scheme, the participants share the secret quantum state by exchanging the secret polarization angles of the disordered travel particles. The security of the secret quantum state is also guaranteed by the non-orthogonal multi-partite-controlled entanglement states, the participants＇ secret polarizations, and the disorder of the travelling particles. Moreover, the present scheme is secure against the particle-number splitting attack and the intercept-and-resend attack. It may be still secure even if the distributed quantum state is embedded in a not-so-weak coherent-state pulse.     

Sufficient and Necessary Conditions of Entanglement Transformations Between Mixed States

Based on a new measure of entanglement for finite-dimensional bi-particle pure states, we give sufficient and necessary conditions that a bi-particle mixed state ρ can be transformed into another mixed state σ by local operations and classical communication (LOCC). This result can be regarded as a generalization of Nielsen’s theorem (Nielsen, Phys. Rev. Lett. 83:436, 1999). However, we find that it is more difficult to determine the entanglement transformations between mixed states than to do between pure ones.     

Entanglement Purification for Mixed Entangled Quantum Dot States via Superconducing Transmission Line Resonators

An entanglement purification protocol for mixed entangled states is presented via double quantum dot molecules inside a superconducing transmission line resonator （TLR）. In the current scenario, coupling for arbitrary double quantum dot molecules can be tuned via the TLR in the large detuning region by controlling the qubit level splitting. The TLR is always empty and only virtually excited, so the interaction is insensitive to both the TLR decay and thermal field. Discussion about the feasibility of our scheme shows that the entanglement purification can be implemented with high fidelity and successful probability.     

Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved

Based on the technique of integration within an ordered product of operators we have demonstrated that singlemode mixed states＇ density matrices can be recast into the normally ordered Gaussian forms [Chin. Phys. Lett. 24 （2007） 3322]. Here we employ the Weyl ordering invariance under similar transformations to show that some two-mode mixed states with entanglement involved can be put into normally ordered form in the bivariate normal distribution too and its marginal distributions can be analysed. In this way, density operators of quantum statistics can be analogous to mathematical statistics, and calculation of variances can be simplified.     

纠缠的纯化和提取

纠缠的纯化和提取在量子信息的理论和实验上都是一个重要的方向，简单回顾了这个方向上的一些主要进展，并重点介绍了有限个拷贝情况下的纠缠提取。提出了准分离态和提取子空间的概念，得到了从一个混合态的有限个拷贝中提取纯纠缠态的必要条件及充要条件；并得到了有限个拷贝情况下的最有效的提取方案；考虑了这些结论在无限个拷贝的情况下的推广。     

Efficient Entanglement Measure for Graph States

International Journal of Theoretical Physics - In this paper, we study the multipartite entanglement properties of graph states up to seven qubits. Our analysis shows that the generalized...     

Entanglement of Formation for Quantum States

We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generallzed concurrence, from the monotonicity and convexity the entanglement of formafion for a class of high-dimensional mixed states has been calculated analytically,     

Two-Photon Spin States and Entanglement States

In this paper, we have given the spin states of two-photon, which are expressed by the quadratic combination of two single-photon spin states, and given all entanglement states of two-photon from the spin states of two-photon. The new expression of two-photon entanglement states should be used in quantum computation and quantum communication.     

Practical Entanglement Concentration for Entangled Coherent States

Entangled coherent state (ECS) is quite important in current quantum communication and quantum computation. In this paper, we discuss two practical entanglement concentration protocols (ECPs) to recover the maximally ECSs from the partially ECSs. In the first ECP, the parties do not need to know the initial coefficients of the partially ECSs. In the second ECP, they should know the initial coefficients. Both protocols are based on the linear optics which make them feasible in current experiment. Especially, in the second ECP, they only require one pair of initial partially ECSs, which makes this ECP optimal. Both ECPs may be useful in current quantum information processing.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Entanglement Swapping for Displaced Two-Mode Squeezed States

We discuss the entanglement swapping of two pairs of displaced two-mode squeezed states and find that the squeezing parameter of the outcoming squeezed state is less than that of the originM squeezed states. The calculation is greatly simplified by virtue of the natural expression of the two-mode squeezing operator in EPR eigenstate representation. A protocol for such entanglement swapping is proposed.``     

Multi-party Quantum Private Comparison Protocol Using d-Dimensional Basis States Without Entanglement Swapping

We present a new multi-party quantum private comparison protocol based on d-dimensional basis states. Different from previous protocols, our protocol have some advantages. n parties can determine wether their private information are equal or not in one time execution of our protocol. Without using the entangled character of d-dimensional basis states, we only need to perform the local unitary operation on particles to encode the information and to get the comparison result. We also discuss that our protocol can withstand various kinds of outside attacks and participant attacks.     

A Novel Scheme for Quantum Teleportation of N-Particle Generalized Bell-Type States Using Minimal Entanglement Resources

In this paper, we present an efficient scheme for the teleportation of an arbitrary N-particle generalized Bell-type state using a single Bell pair as entanglement channel. For odd and even N-particle states the scheme slightly differs and it is discussed in detail for the simplest cases, 3 and 4 particle states. Further, we have compared the quantum cost of our scheme with other teleportation schemes which use a single Bell pair as entanglement channel.

     

Separable States to Distribute Entanglement

It was shown [Cubitt et al. in Phys. Rev. Lett. 91: 037902, 2003] that two distant particles can be entangled by sending a third particle never entangled with the other two. In this paper, we present classes of multi-qubit separable states to distribute entanglement by the same way, and investigate the classes. Furthermore, we calculate the maximal amount of entanglement which two parties of separable states in the classes can have after applying the way.     

Schmidt Number Entanglement Measure for Multipartite k-nonseparable States

In this paper, an entanglement measure for multipartite quantum states with respect to k-partition was introduced, which is called Schmidt number entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-ME SN. We show that this measure is well-defined, i.e., it satisfies some basic properties as an entanglement measure. In addition, we give a super bound and lower bound of k-ME SN for multipartite pure states according to the definition of joint k-Schmidt number with respect to k-partition. Furthermore, we give some examples to show that Schmidt number entanglement measure can quantify the strength of entanglement for multipartite quantum states.

     

Tractable Quantification of Entanglement for Multipartite Pure States

We present kth-order entanglement measure and global kth-order entanglement measure for multipartite pure states, and extend Bennett＇s measure of partial entropy for bipartite pure states to a multipaxtite case. These measures are computable and can effectively classify and quantify the entanglement of multipartite pure states.     

Relativity of Pure States Entanglement

Entanglement of any pure state of an N×N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N≥3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the “Future,” the “Past,” and the set of noncomparable states.