Universal resources for approximate and stochastic measurement-based quantum computation

We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation, in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting e.g. from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained for the exact, deterministic case can be lifted to the much more general approximate, stochastic case, moving from the idealized situation considered in previous works, to the practically relevant context of non-perfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We provide examples of resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high degree of geometric entanglement as universal resources.Comment: 17 pages; abstract shortened with respect to the published version to respect the arXiv limit of 1,920 character

Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices

We describe a general technique that allows to induce and control strong interaction between spin states of neighboring atoms in an optical lattice. We show that the properties of spin exchange interactions, such as magnitude, sign, and anisotropy can be designed by adjusting the optical potentials. We illustrate how this technique can be used to efficiently ``engineer'' quantum spin systems with desired properties, for specific examples ranging from scalable quantum computation to probing a model with non-trivial topological orders that supports exotic non-abelian anyonic excitations.Comment: 5 pages, 2 figures, revte

Multiparticle entanglement purification for two-colorable graph states

We investigate multiparticle entanglement purification schemes which allow one to purify all two colorable graph states, a class of states which includes e.g. cluster states, GHZ states and codewords of various error correction codes. The schemes include both recurrence protocols and hashing protocols. We analyze these schemes under realistic conditions and observe for a generic error model that the threshold value for imperfect local operations depends on the structure of the corresponding interaction graph, but is otherwise independent of the number of parties. The qualitative behavior can be understood from an analytically solvable model which deals only with a restricted class of errors. We compare direct multiparticle entanglement purification protocols with schemes based on bipartite entanglement purification and show that the direct multiparticle entanglement purification is more efficient and the achievable fidelity of the purified states is larger. We also show that the purification protocol allows one to produce private entanglement, an important aspect when using the produced entangled states for secure applications. Finally we discuss an experimental realization of a multiparty purification protocol in optical lattices which is issued to improve the fidelity of cluster states created in such systems.Comment: 22 pages, 8 figures; replaced with published versio

Single-Photon Generation from Stored Excitation in an Atomic Ensemble

Single photons are generated from an ensemble of cold Cs atoms via the protocol of Duan et al. [Nature \textbf{414}, 413 (2001)]. Conditioned upon an initial detection from field 1 at 852 nm, a photon in field 2 at 894 nm is produced in a controlled fashion from excitation stored within the atomic ensemble. The single-quantum character of the field 2 is demonstrated by the violation of a Cauchy-Schwarz inequality, namely $w(1_{2},1_{2}|1_{1})=0.24\pm 0.05\ngeq 1$, where $w(1_{2},1_{2}|1_{1})$ describes detection of two events $(1_{2},1_{2})$ conditioned upon an initial detection $1_{1}$, with $w\to 0$ for single photons.Comment: 5 pages, 4 figure

Quantum communication cost of preparing multipartite entanglement

We study the preparation and distribution of high-fidelity multi-party entangled states via noisy channels and operations. In the particular case of GHZ and cluster states, we study different strategies using bipartite or multipartite purification protocols. The most efficient strategy depends on the target fidelity one wishes to achieve and on the quality of transmission channel and local operations. We show the existence of a crossing point beyond which the strategy making use of the purification of the state as a whole is more efficient than a strategy in which pairs are purified before they are connected to the final state. We also study the efficiency of intermediate strategies, including sequences of purification and connection. We show that a multipartite strategy is to be used if one wishes to achieve high fidelity, whereas a bipartite strategy gives a better yield for low target fidelity.Comment: 21 pages, 17 figures; accepted for publication in Phys. Rev. A; v2: corrections in figure