Quantum nonlocality of generic family of four-qubit entangled pure states

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states |Gabcd[Phys. Rev. A 65 052112(2002)] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called "four-qubit the maximally entangled state |Gm" and it is also violated by four-qubit W state and a special family of states |Gab00. Moreover, a useful entanglement-nonlocality relationship for the family of states |Gab00is derived. Finally, we present a scheme of preparation of the state |Gmwith linear optics and cross-Kerr nonlinearities.     

Generation of hyperentangled photon pairs

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.     

Experimental violation of a cluster state bell inequality

Cluster states are a new type of multiqubit entangled states with entanglement properties exceptionally well suited for quantum computation. In the present work, we experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism. This exploration is based on a recently derived Bell-type inequality [V. Scarani et al., Phys. Rev. A 71, 042325 (2005)] which is tailored, by using a combination of three- and four-particle correlations, to be maximally violated by cluster states but not violated at all by GHZ states. We observe a cluster-state Bell parameter of 2.59+/-0.08, which is more than 7sigma larger than the threshold of 2 imposed by local realism.     

三比特类GHZ态的Bell型不等式和非定域性

研究了一般形式类GHZ(Greenberger-Horne-Zeilinger)态的共生纠缠度及非定域性, 给出了类GHZ纠缠态的共生纠缠、Mermin不等式和Svetlichny不等式的解析表达式, 并通过数值计算讨论纠缠与非定域性之间的关系. 结果表明, 类GHZ纠缠态的共生纠缠和两个Bell型不等式描述的非定域性是一致的, Bell算符及其参量, 能够明显展示量子态的非定域特性. 关键词： 量子信息 类GHZ态 共生纠缠 Bell型不等式     

Experimental Investigation of the Robustness of a New Bell-Type Inequality of Triphoton GHZ States in Open Systems

Knowing the level of entanglement robustness against quantum bit loss or decoherence mechanisms is an important issue for any application of quantum information. Fidelity of states can be used to judge whether there is entanglement in multi-particle systems. It is well known that quantum channel security in QKD can be estimated by measuring the robustness of Bell-type inequality against noise. We experimentally investigate a new Bell-type inequality (NBTI) in the three-photon Greenberger–Horne–Zeilinger (GHZ) states with different levels of spin-flip noise. The results show that the fidelity and the degree of violation of the NBTI decrease monotonically with the increase of noise intensity. They also provide a method to judge whether there is entanglement in three-particle mixed states.     

Testing the nonlocality of entangled states by a new Bell-like inequality

We test a new four-qubit entangled state by the former Bell-like inequalities and find that it violates these inequalities, but not maximally. According to this entangled state, we build a new Bell-like inequality, which is violated by this new state maximally. We also determine the nonlocality of some other four-qubit states by the new inequality. It is found that the new inequality acts as a strong entanglement witness for the new state. This can be used to test new entangled states experimentally.     

Entanglement Swapping for Cluster-Class States and Its Applications in Quantum Information Processing

Entanglement swapping for four-qubit cluster-class states is studied. It is shown that a four-qubit cluster state (maximally entangled) can be obtained with a certain probability from two four-qubit cluster-class states by entanglement swapping. The probability is related to the smallest superposition coefficient of the cluster-class states (when all the moduli of amplitudes are equivalent, they are the usual cluster states and the probability hits to one). Two examples for the applications of the entanglement swapping are also presented. One is quantum teleportation of an arbitrary two-qubit state via a quantum repeater, in which the success probability can be improved by the entanglement swapping when the quantum channels are general cluster-class states (partially entangled). The other is quantum key distribution, in which a secret random sequence of bits (a “key”) can be efficiently established between two distant parties by the entanglement swapping of two groups of cluster states.     

A proposal to test Bell’s inequalities with mesoscopic non-local states in cavity QED

We propose a cavity quantum electrodynamics (CQED) experiment to test the violation of a Bell-type inequality using non-local mesoscopic states (NLMS). These states involve coherent field superpositions stored in two spatially-separated high-Q cavities. The inequality is expressed in terms of the measured Wigner function of the entangled two-field-mode system at four points in phase space, as proposed in [Banaszek and Wódkiewicz, Phys. Rev. Lett. 82, 2009 (1999)]. We examine the production of these entangled NLMS and the measurement of their Wigner function. The experiment involves circular Rydberg atoms and superconducting millimeter-wave cavities. We present a detailed numerical study of the optimal inequality violation and of the effect of decoherence. We discuss the range of experimental parameters making it possible to observe a locality violation and show that they correspond to realistic, albeit demanding, conditions.     

Separability criterion for quantum effects

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) inequality for quantum states. The violation of the dual version of the Bell–CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

Continuous Variable Entanglement and Violation of Bell Inequality for Two Modes in a Three-Level Cascade Atomic System

Continuous variable entanglement and violation of Bell inequality for two modes are investigated in a three-level cascade atomic system. Entanglement of the system is demonstrated according to the entanglement criterion [Phys. Rev. Lett. 84 （2000）2722]. Violation of Bell inequality is studied within the framework of a quantum theory of multiwave mixing. It is shown that there are some states that are entangled but do not violate the Bell inequality.     

Entanglement witnesses of four-qubit tripartite separable quantum states

A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.     

Bell inequality violation with two remote atomic qubits

We observe violation of a Bell inequality between the quantum states of two remote Yb+ ions separated by a distance of about 1 m with the detection loophole closed. The heralded entanglement of two ions is established via interference and joint detection of two emitted photons, whose polarization is entangled with each ion. The entanglement of remote qubits is also characterized by full quantum state tomography.     

Experimental bound entanglement in a four-photon state

Bound entanglement is central to many exciting theoretical results in quantum information processing, but has thus far not been experimentally realized. In this work, we consider a one-parameter family of four-qubit Smolin states. We experimentally produce these states in the polarization of four optical photons produced from parametric down-conversion. Within a range of the parameter, we show that our states are entangled and undistillable, and thus bound entangled. Using these bound-entangled states we demonstrate entanglement unlocking.     

Entanglement Swapping in the Presence of White and Color Noise

The influence of white and color noise on the outcome of the entanglement swapping process is investigated in a four-qubit system. Critical degree of noise in initial state, that could destroy entanglement in a result state is presented. The entanglement characteristics, such as concurrence, tangle, etc. are compared. Results could be helpful for experiments regarding entanglement swapping as conditions for initial quantum entangled states, to obtain entangled result state.     

Photonic Four-qubit Entangled Decoherence-free States Assisted by Cavity-QED System

We propose an efficient preparation of photonic four-qubit entangled decoherence-free states assisted by the cavity-QED system. By using the optical selection rule derived by a single electron charged self-assembled GaAs/InAs quantum dot in a micropillar resonator, two photons are used to generate four-qubit entangled decoherence-free states. Compared with previous entanglement based photonic protocols, the present one requires single-photon resources and is deterministic. These states may be applied to long-distance communications because only two photons are transmitted.     

Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

Four-qubit entanglement has been investigated using a recent proposed entanglement measure, multiple entropy measures （MEMS）. We have performed optimization for the nine different families of states of four-qubit system. Some extremal entangled states have been found.     

Multipartite entanglement inequalities via spin vector geometry

We introduce inequalities for multipartite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found.     

Classifying N-qubit entanglement via Bell's inequalities

All the states of N qubits can be classified into N-1 entanglement classes from 2-entangled to N-entangled (fully entangled) states. Each class of entangled states is characterized by an entanglement index that depends on the partition of N. The larger the entanglement index of a state, the more entangled or the less separable is the state in the sense that a larger maximal violation of Bell's inequality is attainable for this class of state.     

Constructing unextendible product bases from multiqubit ones

The construction of multipartite unextendible product bases(UPBs) is a basic problem in quantum information.We respectively construct two families of 2 × 2× 4 and 2 × 2 × 2 × 4 UPBs of size eight by using the existing four-qubit and five-qubit UPBs.As an application,we construct novel families of multipartite positive-partial-transpose entangled states,as well as their entanglement properties in terms of the geometric measure of entanglement.