Related papers: Orthomodular Lattices and a Quantum Algebra

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…

The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

We define the Wajsberg-center and the OML-center of a quantum-Wajsberg algebra, and study their structures. We prove that the Wajsberg-center is a Wajsberg subalgebra of a quantum-Wajsberg algebra, and that it is a distributive sublattice…

Let $L$ be an even (positive definite) lattice and $g\in O(L)$. In this article, we prove that the orbifold vertex operator algebra $V_{L}^{\hat{g}}$ has group-like fusion if and only if $g$ acts trivially on the discriminant group…

A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…

We provide several new results on quantum state space, on lattice of subspaces of an infinite dimensional Hilbert space, and on infinite dimensional Hilbert space equations as well as on connections between them. In particular we obtain an…

We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…

We study to what extent quantum algorithms can speed up solving convex optimization problems. Following the classical literature we assume access to a convex set via various oracles, and we examine the efficiency of reductions between the…

In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…

We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged)…

We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. The method is based on using the defects in the lattice, wherever…

This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…

The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping…

We show that, for every orthogonal lub-complete poset P, we can introduce multiple-valued implications sharing properties with quantum implications presented for orthomodular lattices by Kalmbach. We call them classical implication,…

We involve a certain propositional logic based on ortholattices. We characterize the implicational reduct of such a logic and we show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence…

For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…

We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of…

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…