Related papers: Duality and tangles of set separations
Sets in R^n in which every pair of elements x, y can be connected by a path in the set of length bounded by a constant multiple of the distance between x and y are considered.
In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.
Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to…
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar…
Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics. Systems that are mapped onto themselves by a duality transformation are called…
We associate to every quandle $X$ and an associative ring with unity $\mathbf{k}$, a nonassociative ring $\mathbf{k}[X]$ following [3]. The basic properties of such rings are investigated. In particular, under the assumption that the inner…
We predict that if internal and momentum states of an interfering object are correlated (entangled), then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with much higher precision than…
We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.
The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the…
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we determined structures that are complementary to arbitrary…
In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…
Entanglement in multipartite systems can be achieved by the coherent superposition of product states, generated through a universal unitary transformation, followed by spontaneous parametric down-conversions and path identification.
The definition of entanglement in identical-particle system is introduced. The separability criterion in two-identical particle system is given. The physical meaning of the definition is analysed. Applications to two-boson and two-fermion…
In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact…
We establish duality for monogamy of entanglement: whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, we prove that the same quantity provides a…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integral $H$, to the given system, by…
Tangle-tree theorems are an important tool in structural graph theory, and abstract separation systems are a very general setting in which tangle-tree theorems can still be formulated and proven. For infinite abstract separation systems, so…