Related papers: States and synaptic algebras
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…
The generalized coherent states attached to the Jacobi group realize the squeezed states. Imposing hermitian conjugacy to the generators of the Jacobi algebra, we find out the form of the weight function appearing in the scalar product. We…
We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.
For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.
Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of…
It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
We first prove that ontological models of the quantum state which are capable of reproducing the Born probability rule and fall in the class of $\psi$-epistemic models are inconsistent with the Sch{\"o}dinger time evolution. We then model…
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
The exceptional Jordan algebra is the algebra of $3\times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan's algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of…
In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on…
This work is concerned with the notion of {eigenstates} for $C^*$-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (\eg dynamical…