Related papers: Topologies on Quantum Effects
A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of the invariance under diffeomorphisms and the realization of the Lie-Rinehart relations between the generators of the…
An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space…
This is a series of lecture notes explaining topos theory and its application in physics.
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
An observable on a quantum structure is any $\sigma$-homomorphism of quantum structures from the Borel $\sigma$-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the…
In this paper we start with the development of a theory of presheaves on a lattice, in particular on the quantum lattice $\LL(\kH)$ of closed subspaces of a complex Hilbert space $\kH$, and their associated etale spaces. Even in this early…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
The topological terms of the bulk effective action for the integer quantum Hall effect, capturing the dynamics of gauge and gravitational fluctuations, reveal a curiosity, namely, the Abelian potential for the magnetic field appears in a…
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…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
The collection of all topologies on the set of three points is studied treating the topology as quantum-like observable. It turns out to be possible under the assumption of the asymmetry between the spaces of bra- and ket-vectors. The…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
An observable effects a schematization of the Quantum event structure by correlating Boolean algebras picked by measurements with the Borel algebra of the real line. In a well-defined sense Boolean observables play the role of…