Implementation of quantum maps by programmable quantum processors

A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We develop a mathematical description for these devices, and apply it to several different examples of processors. The problem of finding a processor that will be able to implement a given set of mappings is also examined, and it is shown that while it is possible to design a finite processor to realize the phase-damping channel, it is not possible to do so for the amplitude-damping channel.Comment: 10 revtex pages, no figure

Quantum-state synthesis of multi-mode bosonic fields: Preparation of arbitrary states of 2-D vibrational motion of trapped ions

We present a universal algorithm for an efficient deterministic preparation of an arbitrary two--mode bosonic state. In particular, we discuss in detail preparation of entangled states of a two-dimensional vibrational motion of a trapped ion via a sequence of laser stimulated Raman transitions. Our formalism can be generalized for multi-mode bosonic fields. We examine stability of our algorithm with respect to a technical noise.Comment: 8 pages, revtex, including 2 ps-figures, section about physical implementation added, references updated, submitted to Phys. Rev. A, computer program available at http://www.savba.sk/sav/inst/fyzi/qo

Quantum synthesis of arbitrary unitary operators

Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for realization of any unitary operator which acts on a (truncated) Hilbert space of a single bosonic mode. In particular, we consider a physical implementation of unitary transformations acting on 1-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the discrete Fourier transform.Comment: 6 RevTeX pages with 3 figures, submitted to Phys.Rev.A, see also http://nic.savba.sk/sav/inst/fyzi/qo

Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric

Linear optics substituting scheme for multi-mode operations

We propose a scheme allowing a conditional implementation of suitably truncated general single- or multi-mode operators acting on states of traveling optical signal modes. The scheme solely relies on single-photon and coherent states and applies beam splitters and zero- and single-photon detections. The signal flow of the setup resembles that of a multi-mode quantum teleportation scheme thus allowing the individual signal modes to be spatially separated from each other. Some examples such as the realization of cross-Kerr nonlinearities, multi-mode mirrors, and the preparation of multi-photon entangled states are considered.Comment: 11 pages, 4 eps-figures, using revtex

Searches at HERA for Squarks in R-Parity Violating Supersymmetry

A search for squarks in R-parity violating supersymmetry is performed in e^+p collisions at HERA at a centre of mass energy of 300 GeV, using H1 data corresponding to an integrated luminosity of 37 pb^(-1). The direct production of single squarks of any generation in positron-quark fusion via a Yukawa coupling lambda' is considered, taking into account R-parity violating and conserving decays of the squarks. No significant deviation from the Standard Model expectation is found. The results are interpreted in terms of constraints within the Minimal Supersymmetric Standard Model (MSSM), the constrained MSSM and the minimal Supergravity model, and their sensitivity to the model parameters is studied in detail. For a Yukawa coupling of electromagnetic strength, squark masses below 260 GeV are excluded at 95% confidence level in a large part of the parameter space. For a 100 times smaller coupling strength masses up to 182 GeV are excluded.Comment: 32 pages, 14 figures, 3 table

Multiplicity Structure of the Hadronic Final State in Diffractive Deep-Inelastic Scattering at HERA

The multiplicity structure of the hadronic system X produced in deep-inelastic processes at HERA of the type ep -> eXY, where Y is a hadronic system with mass M_Y< 1.6 GeV and where the squared momentum transfer at the pY vertex, t, is limited to |t|<1 GeV^2, is studied as a function of the invariant mass M_X of the system X. Results are presented on multiplicity distributions and multiplicity moments, rapidity spectra and forward-backward correlations in the centre-of-mass system of X. The data are compared to results in e+e- annihilation, fixed-target lepton-nucleon collisions, hadro-produced diffractive final states and to non-diffractive hadron-hadron collisions. The comparison suggests a production mechanism of virtual photon dissociation which involves a mixture of partonic states and a significant gluon content. The data are well described by a model, based on a QCD-Regge analysis of the diffractive structure function, which assumes a large hard gluonic component of the colourless exchange at low Q^2. A model with soft colour interactions is also successful.Comment: 22 pages, 4 figures, submitted to Eur. Phys. J., error in first submission - omitted bibliograph

Differential (2+1) Jet Event Rates and Determination of alpha_s in Deep Inelastic Scattering at HERA

Events with a (2+1) jet topology in deep-inelastic scattering at HERA are studied in the kinematic range 200 < Q^2< 10,000 GeV^2. The rate of (2+1) jet events has been determined with the modified JADE jet algorithm as a function of the jet resolution parameter and is compared with the predictions of Monte Carlo models. In addition, the event rate is corrected for both hadronization and detector effects and is compared with next-to-leading order QCD calculations. A value of the strong coupling constant of alpha_s(M_Z^2)= 0.118+- 0.002 (stat.)^(+0.007)_(-0.008) (syst.)^(+0.007)_(-0.006) (theory) is extracted. The systematic error includes uncertainties in the calorimeter energy calibration, in the description of the data by current Monte Carlo models, and in the knowledge of the parton densities. The theoretical error is dominated by the renormalization scale ambiguity.Comment: 25 pages, 6 figures, 3 tables, submitted to Eur. Phys.

Measurements of Transverse Energy Flow in Deep-Inelastic Scattering at HERA

Measurements of transverse energy flow are presented for neutral current deep-inelastic scattering events produced in positron-proton collisions at HERA. The kinematic range covers squared momentum transfers Q^2 from 3.2 to 2,200 GeV^2, the Bjorken scaling variable x from 8.10^{-5} to 0.11 and the hadronic mass W from 66 to 233 GeV. The transverse energy flow is measured in the hadronic centre of mass frame and is studied as a function of Q^2, x, W and pseudorapidity. A comparison is made with QCD based models. The behaviour of the mean transverse energy in the central pseudorapidity region and an interval corresponding to the photon fragmentation region are analysed as a function of Q^2 and W.Comment: 26 pages, 8 figures, submitted to Eur. Phys.