Related papers: Structures on the way from classical to quantum sp…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
We present a classical analog of the quantum metric tensor, which is defined for classical integrable systems that undergo an adiabatic evolution governed by slowly varying parameters. This classical metric measures the distance, on the…
We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum…
This is the second part in a series of papers presenting a theory of tensor products for module categories for a vertex operator algebra. In Part I (hep-th/9309076), the notions of $P(z)$- and $Q(z)$-tensor product of two modules for a…
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric…
We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…
We introduce and explore the theory of tensor products in the category of local operator systems. Analogous to minimal operator system OMIN and maximal operator system OMAX, minimal and maximal local operator system structures LOMIN and…
In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we…
In this paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the…
A finite dimensional quantum mechanical system is modeled by a density rho, a trace one, positive semi-definite matrix on a suitable tensor product space H[N] . For the system to demonstrate experimentally certain non-classical behavior,…
Slow convergence of cyclic projections implies divergence of random projections and vice versa. Let $L_1,L_2,\dots,L_K$ be a family of $K$ closed subspaces of a Hilbert space. It is well known that although the cyclic product of the…
The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this…
The aim of this paper is two-fold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly, we discuss the existence of…