Related papers: Characteristic functions under series and parallel…
Quantum parallelism is the main feature of quantum computation. In 1985 D. Deutsch showed that a single quantum computation may be sufficient to state whether a two-valued function of a two-valued variable is constant or not. Though the…
We review various aspects of the characteristic initial value problem for the Einstein equations, presenting new approaches to some of the issues arising.
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
In his deep and prolific investigations of heat diffusion, Lam\'e was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular he derived explicit results for the…
This is a survey of our results on the theory of $n$-homomorphisms of Buchstaber--Rees and its generalization that we obtained. In short, we are concerned with classes of linear maps between commutative rings that can be described the "next…
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of…
We begin with the characterization of quantum graphs as left ideals in $\mathcal M \otimes_{eh} \mathcal M$ (the extended Haagerup tensor product of $\mathcal M$ with itself) to avoid technicalities surrounding representation dependence of…
In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we…