Related papers: The Lamplighter Group
We evaluate the one-shot entanglement of assistance for an arbitrary bipartite state. This yields another interesting result, namely a characterization of the one-shot distillable entanglement of a bipartite pure state. This result is shown…
A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular $m$-tree. We prove that if $G$ is a subgroup of an automata group, then for each finitely generated…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
Associating a physical process with the pure entangled state 1/sqrt 2 (|00> + |11>) is an idealization unless the pair is so prepared using an appropriate quantum gate operating on a known state. Questions related to the reference frame for…
The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of…
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
A simple system composed of electronic oscillators capable of emitting and detecting light-pulses is studied. The oscillators are biologically inspired, their behavior is designed for keeping a desired light intensity, W, in the system.…
A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…
Two possible realizations of the formal neuron are considered as quantum system. The first type complies with classical system. The second type vastly increases the possible problems.
Brou\'e, Malle and Michel have shown that the automizer of an abelian Sylow p-subgroup in a finite simple Chevalley group is an irreducible complex reflection group, for p not too small and different from the defining characteristic. The…
An overview of one- and two-dimensional quantum spin systems based on transition-metal oxides and halides of current interest is given, such as spin-Peierls, spin-dimer, geometrically frustrated and ladder systems. The most significant and…
We construct a Ramsey class whose objects are Steiner systems. In contrast to the situation with general $r$-uniform hypergraphs, it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose: one…
We study the excitation of a two-level system (2LS) by quantum light, thereby bringing our previous studies~(see part~I. of this series) to a target that is quantum itself. While there is no gain for the quantum state of the target as…
Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbers. The same holds for a Sylow 2-subgroup of C.
This is a concise introduction to the theory of Lie groupoids, with emphasis in their role as models for stacks. After some preliminaries, we review the foundations on Lie groupoids, and we carefully study equivalences and proper groupoids.…
We are generalizing in two non-trivial ways the recently defined perspective Abelian groups to the so-called IC-groups and TP-groups, respectively, and obtain numerous results in these two directions that can be viewed as improvements on…
A general scheme to seek for the relations between entanglement and bservables is proposed in principle. In two-qubit systems with enough general Hamiltonian, we find the entanglement to be the functions of observables for six kinds of…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We…
In this paper we characterize when a Cayley automaton semigroup is a group, is trivial, is finite, is free, is a left zero semigroup, or is a right zero semigroup.