Related papers: Invariants, Kronecker Products, and Combinatorics …
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
We discuss a problem initially thought for the Mathematical Olympiad but which has several interpretations. The recurrence sequences involved in this problem may be generalized to recurrence sequences related to a much larger set of…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
This article addresses broad trends in interdisciplinary research in physics where interactions with colleagues in fields such as computer science, ecology, or economics can often be derailed by unintentional clashes of methodologies and…
This paper is concerned with the analysis of linear quantum optical networks. It provides a systematic approach to the construction a model for a given quantum network in terms of a system of quantum stochastic differential equations. This…
We investigate a family of Diophantine polynomial equations which involve continuant functions. In particular, given a polynomial $P(x)\in \mathbb{Z}[x]$ and $n\in \mathbb{N}$, we consider the equation $P(K_n(x_1,\ldots, x_n)) =…
This paper surveys and develops links between polynomial invariants of finite groups, factorization theory of Krull domains, and product-one sequences over finite groups. The goal is to gain a better understanding of the multiplicative…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…
We associate at each link a connectivity space which describes its splittability properties. Then, the notion of order for finite connectivity spaces results in the definition of a new numerical invariant for links, their connectivity…
In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
The entanglement of open curves in 3-space appears in many physical systems and affects their material properties and function. A new framework in knot theory was introduced recently, that enables to characterize the complexity of…
The classical tools which ensure the completeness of vector fields and second order differential equations for mechanical systems are revisited. Possible extensions in three directions are discussed: infinite dimensional Banach and Hilbert…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
These notes are an expanded version of a talk given by the second author. Our main interest is focused on the challenging problem of computing Kronecker coefficients. We decided, at the beginning, to take a very general approach to the…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given…