Related papers: Tensor Products in Quantum Functional Analysis: th…
A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and…
Two pertinent questions for any support theory of a monoidal triangulated category are whether it is functorial and if the tensor product property holds. To this end, we consider the complete prime spectrum of an essentially small monoidal…
We give a characterization of the operators on the injective tensor product $E \hat{\otimes}_\varepsilon X$ for any separable Banach space $E$ and any (non-separable) Banach space $X$ with few operators, in the sense that any operator $T: X…
We develop a new projected wave function approach which is based on projection operators in the form of matrix-product operators (MPOs). Our approach allows to variationally improve the short range entanglement of a given trial wave…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…
A convenient technique for calculating completed topological tensor products of functional Frechet and DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…
Applying Gaussian processes (GPs) to very large datasets remains a challenge due to limited computational scalability. Matrix structures, such as the Kronecker product, can accelerate operations significantly, but their application commonly…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann's foundational works in the thirties. The absence of a suitable quaternionic version of spectrum prevented the full…
We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or…
In recent years finite tensor products of reproducing kernel Hilbert spaces (RKHSs) of Gaussian kernels on the one hand and of Hermite spaces on the other hand have been considered in tractability analysis of multivariate problems. In the…
We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely-positive process with no a priori information about the process apart from the dimension of the system on which the process…
We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…
The paper presents a model-independent, nonperturbative proof of operator product expansions in quantum field theory. As an input, a recently proposed phase space condition is used that allows a precise description of point field…
We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference…
We obtain a far-reaching generalization (in several directions) of the theorem of A. Lambert on the existence of the projective tensor product of operator sequence spaces. This result is obtained in the context of spaces, generalizing…
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…