Related papers: The Lamplighter Group
The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families…
We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…
I present a case for proposed future linear and circular lepton colliders as ideal machines for understanding and exploration. As machines for understanding, they provide unprecedented tools for studying the Higgs and observing phenomena…
In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce…
Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to…
In a previous paper with Kashyap we generalized the theory of $W^*$-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak*-rigged modules. The present paper and its contemporaneous…
We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states.…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
We produce a connected real Lie group that, as a first order structure in the group language, interprets the real field expanded with a predicate for the integers. Moreover, the domain of our interpretation is definable in the group.
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
We report,to the best of our knowledge, the first observation of concentrating paraxial beams of light in a linear nondispersive medium. We have generated this intriguing class of light beams, recently predicted by one of us, in both one-…
We examine the anyon representation of the Laughlin quasi-holes, in particular the one-dimensional, algebraic aspects of the representation. For the cases of one and two quasi-holes an explicit mapping to anyon systems is given, and the…
Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.
The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…
This is a rather personal introductory outline of an interesting class of geometric, resp. graph- and group-theoretical structures. After an introductive section about their genesis, the general construction of horocyclic products is…
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…
We have classified, upto isoclinism, certain groups with a given central factor. As an application, we classify, upto isoclinism, groups having at the most nine element centralizers. Among other results of independent interest, we have…
We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
Consistency with relativistic causality narrows down dramatically the class of measurable observables. We argue that by weakening the preparation role of ideal measurements, many of these observables become measurable. Particularly, we show…