We consider pure quantum states of N ≫ 1 spins or qubits and study the average entanglement that can be localized between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this localizable entanglement, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.PACS numbers: 03.67. Mn, 73.43.Nq, 05.50.+q The mathematical description of multiparticle quantum systems plays an important role in several branches of physics. The main difficulty stems from the fact that the number of parameters needed to describe a quantum state grows exponentially with the number of particles. However, sometimes it is possible to capture the most relevant physical properties by describing these systems in terms of very few parameters. This is the case, for example, in quantum statistics, where two-particle correlations play a fundamental role. They allow us to understand several complex physical phenomena, like phase transitions. Furthermore, they give rise to concepts like correlation length, which quantifies a very intuitive property of these systems.Multiparticle systems are also of central interest in the field of quantum information and, in particular, the quantification of the entanglement contained in quantum states. The reason is that entanglement is the physical resource to perform some of the most important quantum information tasks, like quantum information transfer (cfr. teleportation) or quantum computation.Given the common interest of quantum statistical mechanics and quantum information in multiparticle systems it is natural to try to describe the physical phenomena, like quantum phase transitions, appearing in (e.g.) spin systems from the point of view of entanglement. The main restriction one encounters is the fact that there exist very few measures of multiparticle entanglement with a clear physical meaning. In any case, since entanglement measures correlations (for pure states), one would expect that reasonable entanglement measures be intimately connected to the correlation functions widely used in the context of quantum statistical mechanics. This is not the case, however, if one studies the behavior of the entanglement of formation between two separate spins after tracing out the rest [1,2,3,4,5]. Although this approach exhibits a very pronounced (universal) behavior of this quantity at the transition point, it rapidly vanishes as the distance between the spins goes beyond 3 or 4, and thus it is not related to the correlations possessed by the state. Note also that the approach by Vidal et al. [6], in which they study the scaling of entanglement of a block of spins with the oth...

We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.

We propose a realistic scheme to create motional entangled states of a few bosonic atoms. It can experimentally be realized with a gas of ultra cold bosonic atoms trapped in a deep optical lattice potential. By simultaneously deforming and rotating the trapping potential on each lattice site it is feasible to adiabatically create a variety of entangled states on each lattice well. We fully address the case of N = 2 and N = 4 atoms per well and identify a sequence of fractional quantum Hall states: the Pfaffian state, the 1/2-Laughlin quasiparticle and the 1/2-Laughlin state. Exact knowledge of the spectrum has allowed us to design adiabatic paths to these states, with all times and parameters well within the reach of current experimental setups. We further discuss the detection of these states by measuring different properties as their density profile, angular momentum or correlation functions.

We propose two schemes for cooling bosonic and fermionic atoms that are trapped in a deep optical lattice. The first scheme is a quantum algorithm based on particle number filtering and state dependent lattice shifts. The second protocol alternates filtering with a redistribution of particles by means of quantum tunnelling. We provide a complete theoretical analysis of both schemes and characterize the cooling efficiency in terms of the entropy. Our schemes do not require addressing of single lattice sites and use a novel method, which is based on coherent laser control, to perform very fast filtering.

We study the spin-dependent conductance of ballistic mesoscopic ring systems in the presence of an inhomogeneous magnetic field. We show that, for the setup proposed, even a small Zeeman splitting can lead to a considerable spin polarisation of the current. Making use of a spin-switch effect [1] we propose a device of two rings connected in series that in principle allows for both creating and coherently controlling spin polarized currents at low temperatures.Since the proposal of the Datta-Das transistor [2] over a decade ago, much effort has been spent on finding an effective mechanism for achieving spin-polarized electron injection into semiconductors [3]. The ability to inject and detect spin-polarized currents in a semiconducting material widens the field of usual magneto-electronics in metals and opens up the intriguing program of performing spin electronics [4] based on nonmagnetic semiconductor devices. Due to the obstacle of the conductivity mismatch [5] it has so far proved difficult to demonstrate polarized spin injection from a ferromagnetic metallic contact into a semiconductor. An alternative approach, which is based on magnetic semiconductors [6,7], gives excellent results concerning the injection efficiencies but has the drawback that it is, at least up to now, restricted to low temperatures. The mechanisms commonly used for creating spin-polarized currents rely on magnetic materials or a large Zeeman splitting in a homogeneous magnetic field [8]. In this work we study ballistic mesoscopic rings with inhomogeneous magnetic fields and show that even a small Zeeman splitting (compared to the Fermi energy) can lead to a considerable spin-polarisation of the current. Usually the Zeeman splitting is exploited to align the spin to the energetically favourable lower Zeeman level. Here we demonstrate that for the presented field texture the electron spin, which occupies the higher Zeeman level, is more likely to align itself with the local field direction and thus contributes to a larger degree to the current. The described effect is most pronounced in the adiabatic regime of strong fields where the electron spin follows the spatially varying direction of the magnetic field. But our numerical calculations show that there also exists a region of moderate field strengths for which a spin-polarisation of about 30% can be achieved. Such spin-injection efficiencies could be realised using GaAs/AlGaAs heterostructures with low carrier densities. This has the advantage that both the injector and a possible spin controlling device, such as the spin-switch [1], can be fabricated from the same material and negative interface effects would be avoided.To be more specific we consider symmetric 1d and 2d ballistic mesoscopic rings with two attached leads as shown in Fig. 1. The chosen magnetic field texture is illustrated in Fig. 2. For the inhomogeneous magnetic field we assume a circular configuration B i ( r) ∼ 1/rφ (in polar coordinates) centered around the inner disk of the microstructure. Such a field can be vie...