Related papers: A noncommutative De Finetti theorem for boolean in…
This paper is concerned with a translation invariant network of identical quantum stochastic systems subjected to external quantum noise. Each node of the network is directly coupled to a finite number of its neighbours. This network is…
We consider a 1-parameter family of self-adjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some cases, one obtains negative energy states which seems to…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
We extend inner fluctuations to spectral triples that do not fulfill the first-order condition. This involves the addition of a quadratic term to the usual linear terms. We find a semi-group of inner fluctuations, which only depends on the…
We exhibit a simple condition under which a finite involutary semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new…
The paper investigates the asymptotic behavior of (non-normalized) traces of certain classes of matrices with non-commutative random variables as entries. We show that, unlike in the commutative framework, the asymptotic behavior of…
In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\leq r\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows to derive factorization properties from symmetries. We explain some…
We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
This paper presents a quantum generalization of the multinomial distribution for the transition probabilities of $m$ identical photons in a $k$-port linear optical interferometer: two multinomial coefficients (one for the input…
We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…
In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…
In this paper, the notion of bi-Boolean independence for non-unital pairs of algebras is introduced thereby extending the notion of Boolean independence to pairs of algebras. The notion of B-$(\ell, r)$-cumulants is defined via a bi-Boolean…