Related papers: Beyond canonical decoupling
We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between…
The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of the Yangian or the quantum affine algebra associated with a complex simple Lie algebra. The unrestricted…
We study restricted homomorphism dualities in the context of classes with bounded expansion. This presents a generalization of restricted dualities obtained earlier for bounded degree graphs and also for proper minor closed classes. This is…
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite…
We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, splitting number, and the existence of certain…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
We propose a mechanism for confinement: analytic continuation beyond infinite coupling in the space of the coupling constant. The analytic continuation is realized by renormalization group flows from the weak to the strong coupling regime.…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed…
In open quantum systems, we directly relate anomalies of higher-form symmetries to the long-range entanglement of any mixed state with such symmetries. First, we define equivalence classes of long-range entanglement in mixed states via…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In…
We consider collections of disjoint simple closed curves in a compact orientable surface which decompose the surface into pairs of pants. The isotopy classes of such curve systems form the vertices of a 2-complex, whose edges correspond to…
We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These…
Recently it was shown that if a given state fulfils the reduction criterion it must also satisfy the known entropic inequalities. Now the questions arises whether on the assumption that stronger criteria based on positive but not completely…
This is a sequel to my paper "The Octagonal PET I: Renormalization and Hyperbolic Symmetry". In this paper we use the renormalization scheme found in the first paper to classify the limit sets of the systems according to their topology. The…
We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to…
A longstanding challenge in the foundations of quantum mechanics is the verification of alternative collapse theories despite their mathematical similarity to decoherence. To this end, we suggest a novel method based on dynamical…
The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…