Mixtures of maximally entangled pure states

We study the conditions when mixtures of maximally entangled pure states remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case of mixing a number of pure states equal to their dimension, we found that the mixed state is entangled provided that the entangled pure states to be mixed are not equally weighted. We also found that one can restrict the set of pure states that one can mix from in order to ensure that the resulting mixed state is genuinely entangled. Also, we demonstrate how these results could be applied as a way to detect entanglement in mixtures of the entangled pure states with noise.     

Teleportation of a Kind of Three-Mode Entangled States of Continuous Variables

A quantum teleportation scheme to teleport a kind of tripartite entangled states of continuous variables by using a quantum channel composed of three bipartite entangled states is proposed. The joint Bell measurement is feasible because the bipartite entangled states are complete and the squeezed state has a natural representation in the entangled state basis. The calculation is greatly simplified by using the Schmidt decomposition of the entangled states.     

Teleportation of a Kind of Three-Mode Entangled States of Continuous Variables

A quantum teleportation scheme to teleport a kind of tripartite entangled states of continuous variables by using a quantum channel composed of three bipartite entangled states is proposed. The joint Bell measurement is feasible because the bipartite entangled states are complete and the squeezed state has a natural representation in the entangled state basis. The calculation is greatly simplified by using the Schmidt decomposition of the entangled states.     

Witness for Non-Quasi Maximally Entangled States

Maximally entangled states, defined as those states that have the maximal entanglement of formation under some entanglement measure, are the ideal resource for many quantum missions. In this paper, we call a convex roof of maximally entangled pure states a quasi maximally entangled state. First, we present the concept of a witness for non-quasi maximally entangled states, which is an observable that can distinguish some non-quasi maximally entangled states from quasi maximally entangled ones. Then we prove that every non-quasi maximally entangled state can be witnessed by a witness and obtain some necessary and sufficient conditions for an observable to be a witness for non-quasi maximally entangled states. Lastly, we give some classes of Hermitian operators, which can become witnesses. Especially, we compute non-quasi maximally entangled states that can be detected by a specific product operator.     

Information under Lorentz Transformation

In the context of quantum information, we investigate extensively some important classes of a general form of a two-qubit system under Lorentz transformation. It is shown Lorentz transformation causes a decay of entanglement and consequently information loses. On the other hand, it generates entangled states between systems prepared initially in a separable states. The partial entangled states are more robust under Lorentz transformation than maximally entangled states. Therefore the rate of information lose is larger for maximum entangled states compared with that for partially entangled states.     

Entanglement and Pancharatnam Phase for Two Two-Level Atoms Interacting with a Single Mode Field

A model of two 2-level atoms interacts with a single quantized electromagnetic field is considered. We study the effect of the mean photon number and the structure of the initial states of the two atoms on the dynamics of the atomic system from the separability point of view. It is found that, if we start from a product mixed atomic state, the probability of generating long living entangled states is increased as the mean photon number increases. Starting from excited atomic system in product state, one generates a more stable entangled states with high degree of entanglement. Also, the effect of the mean photon number on atomic system prepared initially in entangled states is investigated. It is found that the entangled state generated from the initially partial entangled states are more robust than those obtained from a maximum entangled state. The Pancharatnam phase for the separable and entangled states is studied under the effect of the mean photon number and the structure of the initial state. We find that for the separable states, the collapses decrease and the amplitude of the revivals is smaller than that for the entangled state, so there are long-living entangled phases. This property give us a great chances to store safely information in entangled state.     

Entangled photon states recovery and cloning via the micro ring resonators and an add/drop multiplexer

We propose a new system of the entangled photon generation and recovery using a Gaussian pulse traveling within the nonlinear micro ring resonators, whereas the cloning feasibility of the entangled photon states via an add/drop multiplexer is also proposed. Firstly, the optimum entangled photon visibility is generated by using the Gaussian pulse in the ring resonators, where the second harmonic pulses are generated by filtering the chaotic signals. Secondly, the small amount of the transmission power is coupled by the add/drop device, whereas the entangled photon states, i.e. cloning states, are regenerated by using the polarization control unit. Results obtained have shown that the recovery entangled photon states can be made and confirmed with the initial states, which means that the cloning of entangled photon states of the initial states is plausible. The amplified entangled photon for state recovery is also discussed.     

Bound entanglement provides convertibility of pure entangled states

I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and W can be interconverted. In general, multipartite settings composed by N distant parties, all N-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.     

Engineering of Multi-Dimensional Entangled States of Photon Pairs Using Hyper-Entanglement

Multi-dimensional entangled states have been proven to be more powerful in some quantum information processes. Down-converted photons from spontaneous parametric down-conversion are used to engineer multi-dimensional entangled states. A kind of multi-degree multi-dimensional Greenberger-Horne-Zeilinger states can also be generated. The hyper-entangled photons are entangled in energy-time, polarization and orbital angular momentum, which is proven to be useful to increase the dimension of systems and to investigate higher-dimensional entangled states.     

Scheme for realizing entanglement concentration via generalized measurements

How to concentrate non-maximally entangled states for quantum communication is a fundamental problem in quantum information. In this paper, we will apply generalized measurements to entanglement concentration of known non-maximally entangled pure states in arbitrary dimensional system. How to design the generalized measurements for the unambiguous discrimination of linearly independent non-orthogonal states is crucial for the concentration of the known non-maximally entangled states. The result shows that, any known non-maximally entangled pure state (for arbitrary dimensional system) can be transformed to the maximally entangled state only by introducing a qubit as ancilla and a joint unitary transformation operation on one of the entangled particles and the ancilla. In addition, because the less entangled state of each fail round will be re-concentrated too, the entanglement waste during the concentration process will be greatly reduced.     

纠缠相干态的纠缠浓缩

利用线性光学元器件对光场量子态进行操纵,可以实现远程的量子纠缠调控和量子通讯.通过分析光学分束器对相干态光场的作用,发现当初始光场态是两个两部分纠缠态的直乘时,让其中的两模通过光学分束器作用后再对其进行光子计数,另外两模将会塌缩到新的纠缠态.基于这个特点,提出了一个实现部分纠缠相干态纠缠浓缩的方案.在这个方案中,两个部分纠缠相干态被用来作为量子信道,通过光学分束器作用后对光场进行光子数探测时,如果测量到光场的两模分别处于奇光子数态和零光子数态,则光场另外的两模将塌缩到最大纠缠态,从而完成纠缠浓缩的过程.计算结果表明,对于纠缠相干态,无论其初始的纠缠是多么微弱,利用这种方法总有一定的几率可以从中提纯出最大纠缠态.     

Entanglement Dynamics of Two Qubits Coupled to a Noise Environment

We study the time evolution of two two-state systems （two qubits） initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherenee.     

第三讲 量子纠缠态

量子纠缠是量子力学的奇妙特性之一 .文章对量子纠缠的历史作了简单回顾 ,介绍了近年来在纠缠的度量和纠缠态的判别及其分类方面的主要进展 .     

利用纠缠交换实现多粒子纠缠态纯化

利用纠缠交换的方法实现了两粒子和三粒子纠缠态的纯化,并将该方法推广到多粒子纠缠态的情况,而且得出在所有的情况下从部分纠缠态获得最大纠缠态的概率均为2|b|2。在此过程中我们只使用了幺正变换和Hadam ard变换,而不需要经典通信。     

Local Copying of <Emphasis Type="Italic">d</Emphasis>×<Emphasis Type="Italic">d</Emphasis>-dimensional Partially Entangled Pure States

We examine the problem of copying a set of orthogonal, entangled partially (non-maximally) bipartite pure states with an entangled blank state under the restriction to local operations and classical communication (LOCC), and show a protocol for copying these states by LOCC. The necessary and sufficient condition for locally copying partially entangled pure states is then represented. As a result, we find that the problem of local copying these entangled states can be regarded to some extent as that of catalytic transformation between them by LOCC.     

Teleportation of Mixture of Diagonal Bell States via Bound Entangled States

We propose a protocol for teleportation of arbitrary mixture of diagonal Bell states, it is shown that the channel can be constructed with either pure maximally entangled states or mixed bound entangled states. We also present protocols to realize the controlled teleportation of mixture of diagonal Bell states via multi-particle mixed states. Our results show that bound entangled states are also important and useful resources in quantum communication tasks.     

Detection of Tripartite Genuine Entanglement by Two Bipartite Entangled States

There are practical motivations to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. Here, the case that the states are two‐qubit Werner states is considered. The intervals of parameters of two‐qubit Werner states are revealed such that the tripartite state is genuinely entangled. Furthermore, we also investigate the lower bound of genuine multipartite entanglement concurrence for tripartite qudit states. Several examples are given to show the effectiveness of the lower bound.     

Blind Quantum Signature with Controlled Four-Particle Cluster States

A novel blind quantum signature scheme based on cluster states is introduced. Cluster states are a type of multi-qubit entangled states and it is more immune to decoherence than other entangled states. The controlled four-particle cluster states are created by acting controlled-Z gate on particles of four-particle cluster states. The presented scheme utilizes the above entangled states and simplifies the measurement basis to generate and verify the signature. Security analysis demonstrates that the scheme is unconditional secure. It can be employed to E-commerce systems in quantum scenario.     

Bound entangled states invariant under Ux

This paper obtains an entangled condition for isotropic-like states by using an atomic map. It constructs a class of bound entangled states from the entangled condition and shows that the partial transposition of the state from the constructed bound entangled class is an edge bound entangled state by using range criterion.     

Entanglement and Decoherence in Two-Dimensional Coherent State Superpositions

A detailed investigation of entanglement in the generalized two-dimensional nonorthogonal states, which are expressed in the framework of superposed coherent states, is presented. In addition to quantifying entanglement of the generalized two-dimensional coherent states superposition, necessary and sufficient conditions for maximality of entanglement of these states are found. We show that a large class of maximally entangled coherent states can be constructed, and hence, some new maximally entangled coherent states are explicitly manipulated. The investigation is extended to the mixed system states and entanglement properties of such mixed states are investigated. It is shown that in some cases maximally entangled mixed states can be detected. Furthermore, the effect of decoherence, due to both cavity losses and noisy channel process, on such entangled states are studied and its features are discussed.