Quantum Hypergraph States

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalised stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.Comment: 9+5 pages, 5 figures, 1 table, published versio

Afterglow lightcurves, viewing angle and the jet structure of gamma-ray bursts

Gamma ray bursts are often modelled as jet-like outflows directed towards the observer; the cone angle of the jet is then commonly inferred from the time at which there is a steepening in the power-law decay of the afterglow. We consider an alternative model in which the jet has a beam pattern where the luminosity per unit solid angle (and perhaps also the initial Lorentz factor) decreases smoothly away from the axis, rather than having a well-defined cone angle within which the flow is uniform. We show that the break in the afterglow light curve then occurs at a time that depends on the viewing angle. Instead of implying a range of intrinsically different jets - some very narrow, and others with similar power spread over a wider cone - the data on afterglow breaks could be consistent with a standardized jet, viewed from different angles. We discuss the implication of this model for the luminosity function.Comment: Corrected typo in Eq. 1

Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He

Defects are believed to play a fundamental role in the supersolid state of 4He. We have studied solid 4He in two dimensions (2D) as function of the number of vacancies n_v, up to 30, inserted in the initial configuration at rho = 0.0765 A^-2, close to the melting density, with the exact zero temperature Shadow Path Integral Ground State method. The crystalline order is found to be stable also in presence of many vacancies and we observe two completely different regimes. For small n_v, up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n_v, the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. In the equilibrated state it is no more possible to recognize vacancies because they mainly transform into quantum dislocations and crystalline order is found almost independent on how many vacancies have been inserted in the initial configuration. The one--body density matrix in this latter regime shows a non decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of incommensurate versus commensurate state loses meaning for solid 4He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in presence of up to 100 vacancies

Computation of microdosimetric distributions for small sites

Object of this study is the computation of microdosimetric functions for sites which are too small to permit experimental determination of the distributions by Rossi-counters. The calculations are performed on simulated tracks generated by Monte-Carlo techniques. The first part of the article deals with the computational procedure. The second part presents numerical results for protons of energies 0.5, 5, 20 MeV and for site diameters of 5, 10, 100 nm