Entangling spins by measuring charge: a parity-gate toolbox

The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyse the parity gate (P-gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with P-gates and show that native networks simplify considerably the resources required for producing multi-qubit entanglement, like n-GHZ states. Other applications include a Bell-state analyser and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin n-GHZ state with linear elements (beam-splitters and local spin-flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct a novel spin CZ-gate by using the mode degrees of freedom as ancillae.Comment: updated to the published versio

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-$N$ space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as $_2F_1$ Gau\ss{} hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using $q$-product and series representations implied by Jacobi's $\vartheta_i$ functions and Dedekind's $\eta$-function. The corresponding representations can be traced back to polynomials out of Lambert--Eisenstein series, having representations also as elliptic polylogarithms, a $q$-factorial $1/\eta^k(\tau)$, logarithms and polylogarithms of $q$ and their $q$-integrals. Due to the specific form of the physical variable $x(q)$ for different processes, different representations do usually appear. Numerical results are also presented.Comment: 68 pages LATEX, 10 Figure

Magnetic charge, angular momentum and negative cosmological constant

We argue that there are no axially symmetric rotating monopole solutions for a Yang-Mills-Higgs theory in flat spacetime background. We construct axially symmetric Yang-Mills-Higgs solutions in the presence of a negative cosmological constant, carrying magnetic charge $n$ and a nonvanishing electric charge. However, these solution are also nonrotating.Comment: 17 pages, LaTeX, 7 figure

Reduction formalism for Dirac fermions on de Sitter spacetime

The reduction formulas for Dirac fermions are derived, using the exact solutions of free Dirac equation on de Sitter spacetime. In the framework of the perturbation theory one studies the Green functions and derive the scatering amplitude in the first orders of perturbation theory.Comment: 12 pages, no figure

Charged-rotating black holes and black strings in higher dimensional Einstein-Maxwell theory with a positive cosmological constant

We present arguments for the existence of charged, rotating black holes in $d=2N+1$ dimensions, with $d\geq 5$ with a positive cosmological constant. These solutions posses both, a regular horizon and a cosmological horizon of spherical topology and have $N$ equal-magnitude angular momenta. They approach asymptotically the de Sitter spacetime background. The counterpart equations for $d=2N+2$ are investigated, by assuming that the fields are independant of the extra dimension $y$, leading to black strings solutions. These solutions are regular at the event horizon. The asymptotic form of the metric is not the de Sitter form and exhibit a naked singularity at finite proper distance.Comment: 21 pages, 9 figure

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the anomalous dimensions to 3-loop order, the massless Wilson coefficients and also different massive operator matrix elements. Starting at 3-loop order, however, also other letters appear in the case of massive operator matrix elements, the so called iterative non-iterative integrals, which are related to solutions based on complete elliptic integrals or any other special function with an integral representation that is definite but not a Volterra-type integral. After outlining the formalism leading to iterative non-iterative integrals,we present examples for both of these cases with the 3-loop anomalous dimension $\gamma_{qg}^{(2)}$ and the structure of the principle solution in the iterative non-interative case of the 3-loop QCD corrections to the $\rho$-parameter.Comment: 13 pages LATEX, 2 Figure

Perfect fluids from high power sigma-models

Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.Comment: 17 pages. Version published in IJGMMP 8 (2011). Added Example 3.4 and 1 referenc

Spin-Dependent Tunneling of Single Electrons into an Empty Quantum Dot

Using real-time charge sensing and gate pulsing techniques we measure the ratio of the rates for tunneling into the excited and ground spin states of a single-electron AlGaAs/GaAs quantum dot in a parallel magnetic field. We find that the ratio decreases with increasing magnetic field until tunneling into the excited spin state is completely suppressed. However, we find that by adjusting the voltages on the surface gates to change the orbital configuration of the dot we can restore tunneling into the excited spin state and that the ratio reaches a maximum when the dot is symmetric.Comment: 4 pages, 3 figure

Awareness of ovarian cancer symptoms and risk factors in a young ethnically diverse British population

Background: Ovarian cancer does not cause many symptoms in the early stages, which is why the majority of cases are of advanced disease. Increasing awareness of ovarian cancer symptoms may lead to earlier diagnosis and improved outcomes. Methods: Participants in Britain completed the Ovarian Cancer Awareness Measure by online survey (n = 459). Results: Our participants were 75% female, 25% male and a young (27.89 ± 11.44 years) ethnically diverse population (40.3% White, 29.3% Asian and 18.0% Black). Individuals recalled 1.24 ± 1.30 symptoms, and recognised 5.96 ± 2.4 symptoms. We found higher levels of recall and recognition compared to previous research possibly due to using an online survey. Recognition was lowest for difficulty eating (39.4%) and persistently feeling full (38.7%). Males had slightly lower symptom recall and recognition than females. Participants incorrectly recalled an irregular menstrual cycle (22.4%) as an ovarian cancer symptom and 67% answered the age of incidence question incorrectly. Suggesting that participants incorrectly associate ovarian cancer as a disease of pre‐menopausal women. Individuals recalled 1.47 ± 1.20 risk factors, and recognised 6.1 ± 2.4 risk factors. Family history of ovarian cancer was recalled by 59% of participants. Recognition was lowest for in vitro fertilisation treatment (23.0%) and talcum powder in the genital area (23.0%). The generic cancer risk factors of alcohol (9.3%) and poor diet (8.8%) were recalled as specific ovarian cancer risk factors. 57.9% of participants incorrectly answered that there is an ovarian cancer screening programme. Suggesting confusion between ovarian and cervical cancer as participants also recalled cervical cancer risk factors of sexually transmitted diseases (6.3%) and human papillomavirus (1.5%). 29.7% of female participants would seek help for an ovarian cancer symptom within 1–2 days. Help seeking was higher in the Black and Asian ethnicities (44.4% and 45.0%; p = 0.018). Conclusion: Awareness of ovarian cancer symptoms is low. Ovarian cancer awareness campaigns should include common misconceptions identified in this research