Space-like separation of entangled quantum states is a central concept in fundamental investigations of quantum mechanics and in quantum communication applications. Optical approaches are ubiquitous in the distribution of entanglement because entangled photons are easy to generate and transmit. However, extending this direct distribution beyond a range of a few hundred kilometres to a worldwide network is prohibited by losses associated with scattering, diffraction and absorption during transmission. A proposal to overcome this range limitation is the quantum repeater protocol, which involves the distribution of entangled pairs of optical modes among many quantum memories stationed along the transmission channel. To be effective, the memories must store the quantum information encoded on the optical modes for times that are long compared to the direct optical transmission time of the channel. Here we measure a decoherence rate of 8 × 10(-5) per second over 100 milliseconds, which is the time required for light transmission on a global scale. The measurements were performed on a ground-state hyperfine transition of europium ion dopants in yttrium orthosilicate ((151)Eu(3+):Y2SiO5) using optically detected nuclear magnetic resonance techniques. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoupling, a coherence time of 370 ± 60 minutes was achieved at 2 kelvin. It has been almost universally assumed that light is the best long-distance carrier for quantum information. However, the coherence time observed here is long enough that nuclear spins travelling at 9 kilometres per hour in a crystal would have a lower decoherence with distance than light in an optical fibre. This enables some very early approaches to entanglement distribution to be revisited, in particular those in which the spins are transported rather than the light.

A systematic calculation for the transition form factors of heavy to light mesons (B, Bs, D, Ds→ π, K, η, ρ, K*, ω, ϕ) is carried out by using light-cone sum rules in the framework of heavy quark effective field theory. The heavy quark symmetry at the leading order of 1/mQexpansion enables us to reduce the independent wave functions and establish interesting relations among form factors. Some relations hold for the whole region of momentum transfer. The meson distribution amplitudes up to twist-4 including the contributions from higher conformal spin partial waves and light meson mass corrections are considered. The CKM matrix elements |Vub|, |Vcs| and |Vcd| are extracted from some relatively well-measured decay channels. A detailed prediction for the branching ratios of heavy to light meson decays is then presented. The resulting predictions for the semileptonic and radiative decay rates of heavy to light mesons (B, Bs, D, Ds→ π, K, η, ρ, K*, ω, ϕ) are found to be compatible with the current experimental data and can be tested by more precise experiments at B-factory, LHCb, BEPCII and CLEOc.

The possibility of a strong a theorem in six dimensions is examined in multiflavor ϕ^{3} theory. Contrary to the case in two and four dimensions, we find that, in perturbation theory, the relevant quantity a[over ˜] increases monotonically along flows away from the trivial fixed point. a[over ˜] is a natural extension of the coefficient a of the Euler term in the trace anomaly, and it arises in any even spacetime dimension from an analysis based on Weyl consistency conditions. We also obtain the anomalous dimensions and beta functions of multiflavor ϕ^{3} theory to two loops. Our results suggest that some new intuition about the a theorem is in order.

We present a general study on exclusive semileptonic decays of heavy (B, D, B s ) to light (π, ρ, K, K * ) mesons in the framework of effective field theory of heavy quark. Transition matrix elements of these decays can be systematically characterized by a set of wave functions which are independent of the heavy quark mass except for the implicit scale dependence. Form factors for all these decays are calculated consistently within the effective theory framework using the light cone sum rule method at the leading order of 1/m Q expansion. The branching ratios of these decays are evaluated, and the heavy and light flavor symmetry breaking effects are investigated. We also give comparison of our results and the predictions from other approaches, among which are the relations proposed recently in the framework of large energy effective theory.

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We use the background-field method and the heat kernel to obtain all counterterms to two-loop order of conformally-coupled multiflavor φ 3 theory in six spacetime dimensions, defined in curved spacetime and with spacetime-dependent couplings. We also include spacetime-dependent mass terms for completeness. We use these results to write a general expression for the trace anomaly. With the use of Weyl consistency conditions we are able to show that the strong a-theorem for a certain natural candidate quantityã is violated in this theory, and obtain a three-loop expression for the coefficient a of the Euler term in the anomaly. *

It is found that, for a periodic XY chain, the competition between periodicity and anisotropy gives rise to more than one phase-transition point at some parameter region. In this paper, the phase diagram of a period-two XY model in a transverse field is discussed. Two phase transitions, the Ising and anisotropy transitions, driven by the anisotropy parameter γ, are studied by singularities of the order parameters, the ground-state energy and the quantum entanglement. These two transitions are of second order and their traits are discussed.

B meson rare decays (B → K(K * )ll and B → K * γ) are analyzed in the framework of effective field theory of heavy quarks. The semileptonic and penguin type form factors for these decays are calculated by using the light cone sum rules (LCSR) method at the leading order of 1/m Q expansion. Four exact relations between the two types of form factors are obtained at the leading order of 1/m Q expansion. Of particular, the relations are found to hold for whole momentum transfer region. We also investigate the validity of the relations resulted from the large energy effective theory (LEET) based on the general relations obtained in the present approach. The branching ratios of the rare decays are presented and their potential importance for extracting the CKM matrix elements and probing new physics is emphasized.