Dual Methods for Lattice Field Theories at Finite Density

We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we show some physical results obtained with this approach. Furthermore we present a technique to study 2-point functions at finite density. Results for the lattice correlators at various chemical potentials are shown and discussed.Comment: 7 pages, 2 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Solving the sign problems of the massless lattice Schwinger model with a dual formulation

We derive an exact representation of the massless Schwinger model on the lattice in terms of dual variables which are configurations of loops, dimers and plaquette occupation numbers. When expressed with the dual variables the partition sum has only real and positive terms also when a chemical potential or a topological term are added -- situations where the conventional representation has a complex action problem. The dual representation allows for Monte Carlo simulations without restrictions on the values of the chemical potential or the vacuum angle.Comment: Several comments added. Final version to appear in Nuclear Physics

Transforming structures by set interpretations

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.Comment: 36 page

Shaping frequency entangled qudits

Quantum entanglement between qudits - the d-dimensional version of qubits - is relevant for advanced quantum information processing and provides deeper insights in the nature of quantum correlations. Encoding qudits in the frequency modes of photon pairs produced by continuous parametric down-conversion enables access to high-dimensional states. By shaping the energy spectrum of entangled photons, we demonstrate the creation, characterization and manipulation of entangled qudits with dimension up to 4. Their respective density matrices are reconstructed by quantum state tomography. For qubits and qutrits we additionally measured the dependency of a d-dimensional Bell parameter for various degrees of entanglement. Our experiment demonstrates the ability to investigate the physics of high-dimensional frequency entangled qu$d$it states which are of great importance for quantum information science.Comment: 17 pages, 3 figure

Versatile shaper-assisted discretization of energy-time entangled photons

We demonstrate the capability to discretize the frequency spectrum of broadband energy-time entangled photons by means of a spatial light modulator to encode qudits in various bases. Exemplarily, we implement three different discretization schemes, namely frequency bins, time bins and Schmidt modes. Entangled qudits up to dimension $d=4$ are then revealed by two-photon interference experiments with visibilities violating a $d$-dimensional Bell inequality.Comment: 22 pages, 11 figure