Related papers: Generating clones with conservative near-unanimity…

Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Buzek and Hillery. Here, we realized the one-to-two qubits Buzek-Hillery cloning machine with linear optical devices. This method relies…

If a finitely generated torsion free group K has the property that all finitely generated subgroups S of K are either small or have growth constant bounded uniformly away from 1 then a non proper HNN extension G of K, that is a semidirect…

A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a…

Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $\mathfrak P$-adic continued fractions satisfying the finiteness property on $K$ for…

We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…

Let $p$ be an odd prime and $k$ be an algebraically closed field with characteristic $p$. Booher and Cais showed that the $a$-number of a $\mathbb Z/p \mathbb Z$-Galois cover of curves $\phi: Y \to X$ must be greater than a lower bound…

Random unitaries are useful in quantum information and related fields, but hard to generate with limited resources. An approximate unitary $k$-design is an ensemble of unitaries with an underlying measure over which the average is close to…

The size $b$ of the smallest bidirectional macro scheme, which is arguably the most general copy-paste scheme to generate a given sequence, is considered to be the strictest reachable measure of repetitiveness. It is strictly lower-bounded…

A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen…

A soft random graph $G(n,r,p)$ can be obtained from the random geometric graph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. The soft random simplicial complexes is a model for random simplicial complexes built over the…

In this paper we establish sharp weighted bounds (Buckley type theorems) for one{sided maximal and fractional integral operators in terms of one{sided $A_p$ characteristics. Appropriate sharp bounds for strong maximal functions, multiple…

The Carath\'eodory number k(K) of a pointed closed convex cone K is the minimum among all the k for which every element of K can be written as a nonnegative linear combination of at most k elements belonging to extreme rays.…

In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of order $p$, where $p$ is a fixed prime. This measure, known as the $p$-width of $G$, is the minimal $k\in \mathbb{N}$ such that any $g\in G$…

For each integer $k \geq 2$, we introduce a sequence of $k$-ary discrete trees constructed recursively by choosing at each step an edge uniformly among the present edges and grafting on "its middle" $k-1$ new edges. When $k=2$, this…

A finite group $G$ is called $k$-factorizable if for every ordered factorization $|G|=a_1\cdots a_k$ into integers each greater than $1$ there exist subsets $A_1,\dots,A_k\subseteq G$ such that $|A_i|=a_i$ for each $i$ and $G=A_1\cdots…

We prove that the group of almost-automorphisms of the infinite rooted regular $d$-ary tree $\mathcal{T}_d$ arises naturally as the Thompson-like group of a so called $d$-ary cloning system. A similar phenomenon occurs for any…

We extend the concept of the relative error to mixed-state cloning and related physical operations, in which the ancilla contains some a priori information about the input state. The lower bound on the relative error is obtained. It is…

Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order q^(1/k). The same also holds when the generating set…

We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…

We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged into a pseudovariety with one basic ternary operation. We…