Related papers: The Bicomplex Tensor Product, a Bicomplex Choi The…
We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of…
We propose a generalisation of Exel's crossed product by a single endomorphism and a transfer operator to the case of actions of abelian semigroups of endomorphisms and associated transfer operators. The motivating example for our…
The task of computing wavefunctions that are accurate, yet simple enough mathematical objects to use for reasoning has long been a challenge in quantum chemistry. The difficulty in drawing physical conclusions from a wavefunction is often…
We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…
We obtain a faithful representation of the twisted tensor product $B\otimes_{\chi} A$ of unital associative algebras, when $B$ is finite dimensional. This generalizes the representations of [C] where $B=K[X]/<X^2-X>$, [GGV] where…
This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties…
An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressions is revealed. The various contracted products of…
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
We consider the matrix-valued generalizations of bipartite tensor product quantum correlations and bipartite infinite-dimensional tensor product quantum correlations, respectively. These sets are denoted by $C_q^{(n)}(m,k)$ and…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…
We study the derived tensor product of the representation rings of subgroups of a given compact Lie group G. That is, given two such subgroups H_1 and H_2, we study the tensor product of the associated representation rings R(H_1) and R(H_2)…
Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…