Knitting distributed cluster state ladders with spin chains

There has been much recent study on the application of spin chains to quantum state transfer and communication. Here we discuss the utilisation of spin chains (set up for perfect quantum state transfer) for the knitting of distributed cluster state structures, between spin qubits repeatedly injected and extracted at the ends of the chain. The cluster states emerge from the natural evolution of the system across different excitation number sectors. We discuss the decohering effects of errors in the injection and extraction process as well as the effects of fabrication and random errors.Comment: To be published in PRA. v2 includes minor corrections as well as an added discussion on refocussin

Spin injection and electric field effect in degenerate semiconductors

We analyze spin-transport in semiconductors in the regime characterized by $T\stackrel{<}{\sim}T_F$ (intermediate to degenerate), where $T_F$ is the Fermi temperature. Such a regime is of great importance since it includes the lightly doped semiconductor structures used in most experiments; we demonstrate that, at the same time, it corresponds to the regime in which carrier-carrier interactions assume a relevant role. Starting from a general formulation of the drift-diffusion equations, which includes many-body correlation effects, we perform detailed calculations of the spin injection characteristics of various heterostructures, and analyze the combined effects of carrier density variation, applied electric field and Coulomb interaction. We show the existence of a degenerate regime, peculiar to semiconductors, which strongly differs, as spin-transport is concerned, from the degenerate regime of metals.Comment: Version accepted for publication in Phys. Rev.

Effect of perturbations on information transfer in spin chains

Spin chains have been proposed as a reliable and convenient way of transferring information and entanglement in a quantum computational context. Nonetheless, it has to be expected that any physical implementation of these systems will be subject to several perturbative factors which could potentially diminish the transfer quality. In this paper, we investigate a number of possible fabrication defects in the spin chains themselves as well as the effect of non-synchronous or imperfect input operations, with a focus on the case of multiple excitation/qubit transfer. We consider both entangled and unentangled states, and in particular the transfer of an entangled pair of adjacent spins at one end of a chain under the mirroring rule and also the creation of entanglement resulting from injection at both end spins.Comment: Journal version fixes last typo

Spin Coulomb drag in the two-dimensional electron liquid

We calculate the spin-drag transresistivity $\rho_{\uparrow \downarrow}(T)$ in a two-dimensional electron gas at temperature $T$ in the random phase approximation. In the low-temperature regime we show that, at variance with the three-dimensional low-temperature result [$\rho_{\uparrow\downarrow}(T) \sim T^2$], the spin transresistivity of a two-dimensional {\it spin unpolarized} electron gas has the form $\rho_{\uparrow\downarrow}(T) \sim T^2 \ln T$. In the spin-polarized case the familiar form $\rho_{\uparrow\downarrow}(T) =A T^2$ is recovered, but the constant of proportionality $A$ diverges logarithmically as the spin-polarization tends to zero. In the high-temperature regime we obtain $\rho_{\uparrow \downarrow}(T) = -(\hbar / e^2) (\pi^2 Ry^* /k_B T)$ (where $Ry^*$ is the effective Rydberg energy) {\it independent} of the density. Again, this differs from the three-dimensional result, which has a logarithmic dependence on the density. Two important differences between the spin-drag transresistivity and the ordinary Coulomb drag transresistivity are pointed out: (i) The $\ln T$ singularity at low temperature is smaller, in the Coulomb drag case, by a factor $e^{-4 k_Fd}$ where $k_F$ is the Fermi wave vector and $d$ is the separation between the layers. (ii) The collective mode contribution to the spin-drag transresistivity is negligible at all temperatures. Moreover the spin drag effect is, for comparable parameters, larger than the ordinary Coulomb drag effect.Comment: 6 figures; various changes; version accepted for publicatio

Mesoporous matrices for quantum computation with improved response through redundance

We present a solid state implementation of quantum computation, which improves previously proposed optically driven schemes. Our proposal is based on vertical arrays of quantum dots embedded in a mesoporous material which can be fabricated with present technology. The redundant encoding typical of the chosen hardware protects the computation against gate errors and the effects of measurement induced noise. The system parameters required for quantum computation applications are calculated for II-VI and III-V materials and found to be within the experimental range. The proposed hardware may help minimize errors due to polydispersity of dot sizes, which is at present one of the main problems in relation to quantum dot-based quantum computation. (c) 2007 American Institute of Physics

Freezing distributed entanglement in spin chains

We show how to freeze distributed entanglement that has been created from the natural dynamics of spin chain systems. The technique that we propose simply requires single-qubit operations and isolates the entanglement in specific qubits at the ends of branches. Such frozen entanglement provides a useful resource, for example for teleportation or distributed quantum processing. The scheme can be applied to a wide range of systems -- including actual spin systems and alternative qubit embodiments in strings of quantum dots, molecules or atoms.Comment: 5 pages, to appear in Phys. Rev. A (Rapid Communication

Geometry induced entanglement transitions in nanostructures

We model quantum dot nanostructures using a one-dimensional system of two interacting electrons. We show that strong and rapid variations may be induced in the spatial entanglement by varying the nanostructure geometry. We investigate the position-space information entropy as an indicator of the entanglement in this system. We also consider the expectation value of the Coulomb interaction and the ratio of this expectation to the expectation of the confining potential and their link to the entanglement. We look at the first derivative of the entanglement and the position-space information entropy to infer information about a possible quantum phase transition.Comment: 3 pages, 2 figures, to appear in Journal of Applied Physic

Hubbard model as an approximation to the entanglement in nanostructures

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in M wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement

Effect of confinement potential geometry on entanglement in quantum dot-based nanostructures

We calculate the spatial entanglement between two electrons trapped in a nanostructure for a broad class of confinement potentials, including single and double quantum dots, and core-shell quantum dot structures. By using a parametrized confinement potential, we are able to switch from one structure to the others with continuity and to analyze how the entanglement is influenced by the changes in the confinement geometry. We calculate the many-body wave function by `exact' diagonalization of the time independent Schr\"odinger equation. We discuss the relationship between the entanglement and specific cuts of the wave function, and show that the wave function at a single highly symmetric point could be a good indicator for the entanglement content of the system. We analyze the counterintuitive relationship between spatial entanglement and Coulomb interaction, which connects maxima (minima) of the first to minima (maxima) of the latter. We introduce a potential quantum phase transition which relates quantum states characterized by different spatial topology. Finally we show that by varying shape, range and strength of the confinement potential, it is possible to induce strong and rapid variations of the entanglement between the two electrons. This property may be used to tailor nanostructures according to the level of entanglement required by a specific application.Comment: 10 pages, 8 figures and 1 tabl

Entanglement and density-functional theory: testing approximations on Hooke's atom

We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial entanglement can be calculated exactly. We analyse how the strength of the confining potential affects the spatial entanglement and how accurately the methods that we introduced reproduce the exact trends. We also compare the results with the outcomes of standard first-order perturbation methods. The accuracies of energies and densities when using these methods are also considered.Comment: 14 pages with 18 figures; corrected typos, corrected expression for first-order energy in section VI and consequently Fig.13, conclusions and other results unaffecte