Contextual Realization of the Universal Quantum Cloning Machine and of the Universal-NOT gate by Quantum Injected Optical Parametric Amplification

A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit and of flipping it into the orthogonal qubit is reported. The adopted experimental apparatus, a Quantum-Injected Optical Parametric Amplifier (QIOPA) is transformed simultaneously into a Universal Optimal Quantum Cloning Machine (UOQCM) and into a Universal NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, will be found to be universal and optimal, i.e. the measured fidelity of both processes F<1 will be found close to the limit values evaluated by quantum theory. A contextual theoretical and experimental investigation of these processes, which may represent the basic difference between the classical and the quantum worlds, can reveal in a unifying manner the detailed structure of quantum information. It may also enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics. PACS numbers: 03.67.-a, 03.65.Ta, 03.65.UdComment: 27 pages, 7 figure

Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix

It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ''modular localization'' is not only useful in order to construct interaction-free nets of local algebras without using non-unique ''free field coordinates'', but also permits the study of properties of localization and braid-group statistics in low-dimensional QFT. It also sheds some light on the string-like localization properties of the 1939 Wigner's ''continuous spin'' representations.We formulate a constructive nonperturbative program to introduce interactions into such an approach based on the Tomita-Takesaki modular theory. The new aspect is the deep relation of the latter with the scattering operator.Comment: 28 pages of LateX, removal of misprints and extension of the last section. more misprints correcte

Problems in Lattice Gauge Fixing

We review many topics and results about numeric gauge fixing in lattice QCD.Comment: 47 pages, 16 eps figures. Review article sent to IJMP

Square lattice Ising model susceptibility: Series expansion method and differential equation for χ(3)\chi^{(3)}

In a previous paper (J. Phys. A {\bf 37} (2004) 9651-9668) we have given the Fuchsian linear differential equation satisfied by $\chi^{(3)}$, the ``three-particle'' contribution to the susceptibility of the isotropic square lattice Ising model. This paper gives the details of the calculations (with some useful tricks and tools) allowing one to obtain long series in polynomial time. The method is based on series expansion in the variables that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the isotropic square lattice Ising model susceptibility $\chi$. The integration rules are straightforward due to remarkable formulas we derived for these variables. We obtain without any numerical approximation $\chi^{(3)}$ as a fully integrated series in the variable $w=s/2/(1+s^{2})$, where $s =sh (2K)$, with $K=J/kT$ the conventional Ising model coupling constant. We also give some perspectives and comments on these results.Comment: 28 pages, no figur

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

On the integrability of Einstein-Maxwell-(A)dS gravity in presence of Killing vectors

We study some symmetry and integrability properties of four-dimensional Einstein-Maxwell gravity with nonvanishing cosmological constant in the presence of Killing vectors. First of all, we consider stationary spacetimes, which lead, after a timelike Kaluza-Klein reduction followed by a dualization of the two vector fields, to a three-dimensional nonlinear sigma model coupled to gravity, whose target space is a noncompact version of $\mathbb{C}\text{P}^2$ with SU(2,1) isometry group. It is shown that the potential for the scalars, that arises from the cosmological constant in four dimensions, breaks three of the eight SU(2,1) symmetries, corresponding to the generalized Ehlers and the two Harrison transformations. This leaves a semidirect product of a one-dimensional Heisenberg group and a translation group $\mathbb{R}^2$ as residual symmetry. We show that, under the additional assumptions that the three-dimensional manifold is conformal to a product space $\mathbb{R}\times\Sigma$, and all fields depend only on the coordinate along $\mathbb{R}$, the equations of motion are integrable. This generalizes the results of Leigh et al. in arXiv:1403.6511 to the case where also electromagnetic fields are present. In the second part of the paper we consider the purely gravitational spacetime admitting a second Killing vector that commutes with the timelike one. We write down the resulting two-dimensional action and discuss its symmetries. If the fields depend only on one of the two coordinates, the equations of motion are again integrable, and the solution turns out to be one constructed by Krasinski many years ago.Comment: 24 pages, uses jheppub.sty. v2: Final version to be published in CQ