Multipartite Entanglement of a Tetrahedron Lattice

Three-dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence C and 4-concurrence C4. The concurrence C and multipartite entanglement G4 depend on different coupling strengths Ji and are decreased when the temperature T is increased. For a symmetric tetrahedron lattice, the concurrence C is symmetric about J1 when J~ is negative while the multipartite entanglement G4 is symmetric about J1 when J2 〈 2. For a regular tetrahedron lattice, the concurrence G of ground state is 1/3 for ferromagnetic case while G = 0 for antiferromagnetic ca.se. However, there is no multipartitc entanglement since C4=0 in a regular tetrahedron lattice. The external magnetic field 13 can increase the maximum value of the concurrence GB and induce two or three peaks in Cn. There is a peak in the multipartite entanglement G4 B when G4B is varied as a function of the temperature T. This peak is mainly induced by the magnetic field B.

Genuine (k,m)-Threshold Controlled Teleportation and Multipartite Entanglement

We propose genuine （k, m）-threshold controlling schemes for controlled teleportation via multi-particle entangled states, where the teleportation of a quantum state from a sender （Alice） to a receiver （Bob） is under the control of m supervisors such that k （k≤ m） or more of these supervisors can help Bob recover the transferred state. By construction, anyone of our quantum channels is a genuine multipartite entangled state of which any two parts are inseparable. Their properties are compared and contrasted with those of the well-known GHZ, W, and linear cluster states, and also several other genuine multipartite entangled states recently introduced in the literature.

Multipartite Entanglement in Heisenberg Model

The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ=±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.

Generating genuine multipartite entanglement via XY-interaction and via projective measurements

We have studied the generation of multipartite entangled states for the superconducting phase qubits. The experiments performed in this direction have the capacity to generate several specific multipartite entangled states for three and four qubits. Our studies are also important as we have used a computable measure of genuine multipartite entanglement whereas all previous studies analyzed certain probability amplitudes. As a comparison, we have reviewed the generation of multipartite entangled states via von Neumann projective measurements.

Precise detection of multipartite entanglement in four- qubit Greenberger-Horne-Zeilinger diagonal states

We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger-Horne-Zeilinger （GHZ） diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.

Multipartite entanglement generation with dipole induced transparency effect in indirectly coupled dipole-microcavity systems

We propose a feasible scheme of generating multipartite entanglement with the dipole induced transparency （D/T） effect in indirectly coupled dipole-microcavity systems. It is shown that the transmission spectrum is closely related with the interference of dipole-microcavity systems, and we can generate different classes of multi- partite entanglement, e.g., the Greenberger-Horne-Zeilinger state, the W state, and the Dicke state, of the di- pole emitters just by choosing an appropriate frequency of the incident photon. Benefiting from the DIT effect, the schemes may work in the bad or low-Q cavity regime only if the large Purcell factor of the dipole-microcavity system is fulfilled, and they are also insensitive to experimental noise, which may be feasible with present acces- sible technology.

Experimental verification of genuine multipartite entanglement without shared reference frames

Quantum entanglement is an essential resource for quantum information processing, either for quantum communication or for quantum computation. The multi- partite case of entanglement, especially the so called gen- uine multipartite entanglement, has significant importance for multipartite quantum information protocols. Thus, it is a natural requirement to experimentally verify multipartite quantum entanglement when performing many quantum int^rmation tasks. However, this is often technically chal- lenging due to the difficulty of building a shared reference lYame among all involved parties, especially when these parties are distant l^om each other. In this paper, we experimentally verify the genuine tripartite entanglement of a three-photon Greenberger-Horne-Zeilinger state without shared reference frames. A high probability 0.79 of successfully verifying the genuine tripartite entanglement is achieved when no reference frame is shared. In the case of sharing only one common axis, an even higher success probability of 0.91 is achieved.

Effect of the dispersion on multipartite continuous-variable entanglement in optical parametric amplifier

Based on the quantum fluctuations, we adopt the method of generalized V1 criterion to investigate multipartite entan- glement characteristics in an optical parametric amplification system with the consideration of dispersion. The nonlinear interaction becomes strong because of the existence of dispersion coefficient σ. Considering the influence of dispersion factor σ, with increasing the pump parameter μ, the value of minimum variance V1 decreases and the squeezing curve nearly equals 1/（1 ＋ μ）. The larger particle number N results in a smaller variance and higher entanglement.

Dissipative preparation of multipartite Greenberger-Horne-Zeilinger states of Rydberg atoms

The multipartite Greenberger-Horne-Zeilinger(GHZ)states play an important role in large-scale quantum information processing.We utilize the polychromatic driving fields and the engineered spontaneous emissions of Rydberg states to dissipatively drive three-and four-partite neutral atom systems into the steady GHZ states,at the presence of the nextnearest neighbor interaction of excited Rydberg states.Furthermore,the introduction of quantum Lyapunov control can help us optimize the dissipative dynamics of the system so as to shorten the convergence time of the target state,improve the robustness against the spontaneous radiations of the excited Rydberg states,and release the limiting condition for the strengths of the polychromatic driving fields.Under the feasible experimental conditions,the fidelities of three-and four-partite GHZ states can be stabilized at 99.24%and 98.76%,respectively.

Two Schemes for Generation of Entanglement for Vibronic Collective States of Multiple Trapped Ions

We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximal1y Greenberger-Horne-Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglernent of multiple coherent and squeezing states with desired amplitudes in a reasonable time.

Continuous Multipartite Entangled Representation and Its Wigner Operator and Marginal Distribution

By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their Schmidt decompositions and give their entangling operators. Furthermore, based on the above analysis we also find the n-mode Wigner operator. In doing so we may identify the physical meaning of the marginal distribution of the Wigner function.

Unconditional preparation of multipartite continuous-variable entangled states among remote parties

We demonstrate that the n-partite continuous-variable entanglement can be unconditionally prepared among n parties that share no common past, from n two-mode squeezed states. Both CHZ-like and cluster-like states can be generated for any nonzero squeezing in the entangled sources. An application of the resulting multipartite entangled state to a teleportation network is illustrated.

Scheme to generate and discriminate a type of multipartite maximally entangled states in ion-trap

This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The maximum entanglement property of these states is examined. It also demonstrates how to discriminate among these states in the ion-trap.

Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation

We deduce entangled fractional Fourier transformation （EFFT） for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.

Teleportation of atomic entangled states with a thermal cavity

We propose a most simple and experimentally feasible scheme for teleporting unknown atomic entangled states in driven cavity quantum electrodynamics （QED）. In our scheme, the joint Bell-state measurement （BSM） is not required, and the successful probability can reach 1.0. Furthermore, the scheme is insensitive to the cavity decay and the thermal field.

Quantum Information Processing in An Array of Fiber Coupled Cavities

We consider a fiber coupled cavity array. Each cavity is doped with a single two-level atom. By treating the atom-cavity systems as combined polaritonie qubits, we can transform it into a polaritonic qubit-qubit array in the dispersive regime. We show that the four fiber coupled cavity open chain and ring can both generate the four qubit W state and cluster state, and can both transfer one and two qubit arbitrary states. We also discuss the dynamical behaviors of the four fiber coupled cavity array with unequal couplings.

Detection of the quantum states containing at most k−1 unentangled particles

There are many different classifications of entanglement for multipartite quantum systems,one of which is based on the number of the unentangled particles.In this paper,we mainly study the quantum states containing at most k−1 unentangled particles and provide several entanglement criteria based on the different forms of inequalities,which can both identify quantum states containing at most k−1 unentangled particles.We show that these criteria are more effective for some states by concrete examples.

Effect of Different Environments on Multipartite Global Discord

We investigate the influences of non-Markovian dissipation and global dephasing process on the dynamical behaviors of global discord among four qubits.We find that for the non-Markovian dissipation model W state is the most robust to decoherence compared to Dicke and GHZ states;however,for the global dephasing model Dicke state is the most robust to decoherence among them.Also the dynamical behaviors of global quantum discord are quite different from that of the multipartite entanglement for the non-Markovian dissipation model,while they are very similar to each other for the global dephasing model.

The entanglement of several graph states

We exactly evaluate the entanglement of a six vertex and a nine vertex graph states which correspond to non ＂two-colorable＂ graphs. The upper bound of entanglement for five vertex ring graph state is improved to 2.9275, less than the upper bound determined by local operations and classical communication. An upper bound of entanglement is proposed based on the definition of graph state.

Air-core fiber distribution of hybrid vector vortex-polarization entangled states

Entanglement distribution between distant parties is one of the most important and challenging tasks in quantum communication.Distribution of photonic entangled states using optical fiber links is a fundamental building block toward quantum networks.Among the different degrees of freedom,orbital angular momentum(OAM)is one of the most promising due to its natural capability to encode high dimensional quantum states.We experimentally demonstrate fiber distribution of hybrid polarization-vector vortex entangled photon pairs.To this end,we exploit a recently developed air-core fiber that supports OAM modes.High fidelity distribution of the entangled states is demonstrated by performing quantum state tomography in the polarization-OAM Hilbert space after fiber propagation and by violations of Bell inequalities and multipartite entanglement tests.The results open new scenarios for quantum applications where correlated complex states can be transmitted by exploiting the vectorial nature of light.