Macroscopic entanglement by entanglement swapping

We present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.     

Recovery of entanglement lost in entanglement manipulation

When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This Letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.     

Polarization entanglement purification using spatial entanglement

We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.     

Evaluation of entanglement measures in spin systems with the random phase approximation

We discuss a general formalism based on the mean field plus random phase approximation (RPA) for the evaluation of entanglement measures in the ground state of spin systems. The method provides a tractable scheme for determining the entanglement entropy as well as the negativity of finite subsystems, which becomes analytic in the case of systems with translational invariance, in one or D dimensions. The approach improves as the spin increases, and also as the interaction range or connectivity increases. Illustrative results for different types of entanglement entropies (single site, block and comb) in the ground state of a small spin lattice with ferromagnetic type XY couplings in a transverse field are shown and compared with the exact numerical result. Effects arising from symmetry breaking at the mean field level are also discussed.     

Modular entanglement

We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.     

Robust entanglement

It is common belief among physicists that entangled states of quantum systems lose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca⁺ ions and observe robust entanglement lasting for more than 20 s.     

Evaluation of polarization entanglement generated by spontaneous parametric downconversion using photon number counting

Spontaneous parametric downconversion (SPDC) is widely used to generate entangled photon pairs; however, multi-pair emissions degrade the quality of the entanglement. We numerically evaluate polarization-entangled photon pairs created by SPDC. The effects of multi-pair emission events on the visibility of two-photon interference and on the fidelity (the probability overlap for ideal and real states) are analyzed using single-photon detectors that can count the number of incoming photons and discard multiphoton events. Compared with conventional threshold single-photon detectors, photon-number resolving single-photon detectors have higher fidelity for the same or lower visibility.     

相位阻尼通道下初始纠缠对纠缠演化的影响

研究了在非惯性系中相位阻尼通道下初始纠缠对纠缠演化的影响.结果发现:与振幅阻尼通道情况不同,当态参数不同而初始纠缠相同时,纠缠演化曲线重合.当Unruh单粒子态包含左右成分时,比只包含右成分时量子消相干现象更加严重,较早地出现了纠缠死亡现象,并且纠缠死亡时刻与初始纠缠无关.     

Multistage entanglement swapping

We report an experimental demonstration of entanglement swapping over two quantum stages. By successful realizations of two cascaded photonic entanglement swapping processes, entanglement is generated and distributed between two photons, that originate from independent sources and do not share any common past. In the experiment we use three pairs of polarization entangled photons and conduct two Bell-state measurements: one between the first and second pair, and one between the second and third pair. This results in projecting the remaining two outgoing photons from pair 1 and 3 into an entangled state, as characterized by an entanglement witness. The experiment represents an important step towards a full quantum repeater where multiple entanglement swapping is a key ingredient.     

Mutual preservation of entanglement

We study a generalized double Jaynes–Cummings (JC) model where two entangled pairs of two-level atoms interact indirectly. We show that there exist initial states of the qubit system so that two entangled pairs are available at all times. In particular, the minimum entanglement in the pairs as a function of the initial state is studied. Finally, we extend our findings to a model consisting of multi-mode atom–cavity interactions. We use a non-Markovian quantum state diffusion (QSD) equation to obtain the steady-state density matrix for the qubits. We show that the multi-mode model also displays dynamical preservation of entanglement.     

Superactivation of bound entanglement

We show that, in a multiparty setting, two nondistillable (bound-entangled) states tensored together can make a distillable state. This is an example of true superadditivity of distillable entanglement. We also show that unlockable bound-entangled states cannot be asymptotically unentangled, providing the first proof that some states are truly bound-entangled in the sense of being both nondistillable and nonseparable asymptotically.     

Universal measure of entanglement

A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined separable state with the same marginals. A generalization of the Schmidt decomposition is developed to implement the separation of correlations for any pure, multipartite state. The measure based on this decomposition is a generalization of the entanglement of formation to multipartite systems, provides an upper bound for the relative entropy of entanglement, and is directly computable on pure states. The example of pure three-qubit states is analyzed in detail, and a classification based on minimal, four-term decompositions is developed.     

Nonlinear entanglement witnesses

Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions. The nonlinearities are of different orders and can be directly measured in experiments, often without any extra effort.     

Local detection of entanglement

We construct an explicit model where it can be established if a two mode pure Gaussian system is entangled or not by acting only on one of the parts that constitute the system. Measuring the dispersion in momentum and the time evolution of the dispersion in position of one particle we can tell if entanglement is present as well as the degree of entanglement of the system.     

Experimental entangled entanglement

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally entangled state. We show theoretically and experimentally that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled entanglement."     

Facets of tripartite entanglement

Tripartite entangled states of systems 1, 2 and 3 involving nonorthogonal states are used to reveal two hitherto unexplored quantum effects. The first shows that kinematic entanglement between the states of 1 and 2 can affect the result of dynamical interaction between 2 and 3, though 1 and 2 may be spatially separated so that they no longer interact. The second shows that if a residual interaction persists between 1 and 2 while 2 interacts with 3 to form an entangled state, the measurement of observables of 1 can be used to determine whether 2 has interacted with 3. This effect occurs even when the measurement on 1 is made long after the residual interaction between 1 and 2 has ceased to act. Such effects resulting from interplay between unitary dynamics and kinematic entanglement have interesting implications. In particular, we discuss the significance as regards what we call the dynamic version of Einstem locality.