261 research outputs found
A quantum computational semantics for epistemic logical operators. Part I: epistemic structures
Some critical open problems of epistemic logics can be investigated in the framework
of a quantum computational approach. The basic idea is to interpret sentences like
âAlice knows that Bob does not understand that Ï is irrationalâ as pieces of quantum information
(generally represented by density operators of convenient Hilbert spaces). Logical
epistemic operators (to understand, to know. . .) are dealt with as (generally irreversible)
quantum operations, which are, in a sense, similar to measurement-procedures. This approach
permits us to model some characteristic epistemic processes, that concern both human
and artificial intelligence. For instance, the operation of âmemorizing and retrieving
informationâ can be formally represented, in this framework, by using a quantum teleportation
phenomenon
Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time
It is known that no length or time measurements are possible in sub-Planckian
regions of spacetime. The Volovich hypothesis postulates that the
micro-geometry of spacetime may therefore be assumed to be non-archimedean. In
this letter, the consequences of this hypothesis for the structure,
classification, and conformal symmetry of elementary particles, when spacetime
is a flat space over a non-archimedean field such as the -adic numbers, is
explored. Both the Poincar\'e and Galilean groups are treated. The results are
based on a new variant of the Mackey machine for projective unitary
representations of semidirect product groups which are locally compact and
second countable. Conformal spacetime is constructed over -adic fields and
the impossibility of conformal symmetry of massive and eventually massive
particles is proved
The structure of classical extensions of quantum probability theory
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called MisraâBugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed
Epistemic quantum computational structures in a Hilbert-space environment
Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like âAlice knows that Bob does not understand that Ï is irrationalâ as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know ...) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artiïŹcial intelligence. For instance, the operation of âmemorizing and retrieving informationâ can be formally represented, in this framework, by using a quantum teleportation phenomenon
The structure of the quantum mechanical state space and induced superselection rules
The role of superselection rules for the derivation of classical probability
within quantum mechanics is investigated and examples of superselection rules
induced by the environment are discussed.Comment: 11 pages, Standard Latex 2.0
Classical statistical distributions can violate Bell-type inequalities
We investigate two-particle phase-space distributions in classical mechanics
characterized by a well-defined value of the total angular momentum. We
construct phase-space averages of observables related to the projection of the
particles' angular momenta along axes with different orientations. It is shown
that for certain observables, the correlation function violates Bell's
inequality. The key to the violation resides in choosing observables impeding
the realization of the counterfactual event that plays a prominent role in the
derivation of the inequalities. This situation can have statistical (detection
related) or dynamical (interaction related) underpinnings, but non-locality
does not play any role.Comment: v3: Extended version. To be published in J. Phys.
Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
The velocity basis of the Poincare group is used in the direct product space
of two irreducible unitary representations of the Poincare group. The velocity
basis with total angular momentum j will be used for the definition of
relativistic Gamow vectors.Comment: 14 pages; revte
Quantization and noiseless measurements
In accordance with the fact that quantum measurements are described in terms
of positive operator measures (POMs), we consider certain aspects of a
quantization scheme in which a classical variable is associated
with a unique positive operator measure (POM) , which is not necessarily
projection valued. The motivation for such a scheme comes from the well-known
fact that due to the noise in a quantum measurement, the resulting outcome
distribution is given by a POM and cannot, in general, be described in terms of
a traditional observable, a selfadjoint operator. Accordingly, we notice that
the noiseless measurements are the ones which are determined by a selfadjoint
operator. The POM in our quantization is defined through its moment
operators, which are required to be of the form , , with
a fixed map from classical variables to Hilbert space operators. In
particular, we consider the quantization of classical \emph{questions}, that
is, functions taking only values 0 and 1. We compare two concrete
realizations of the map in view of their ability to produce noiseless
measurements: one being the Weyl map, and the other defined by using phase
space probability distributions.Comment: 15 pages, submitted to Journal of Physics
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