45 research outputs found
Boundedness of completely additive measures with application to 2-local triple derivations
We prove a Jordan version of Dorofeev's boundedness theorem for completely
additive measues and use it to show that every (not necessarily linear nor
continuous) 2-local triple derivation on a continuous JBW*-triple is a triple
derivation.Comment: 30 page
Different Types of Conditional Expectation and the Lueders - von Neumann Quantum Measurement
In operator algebra theory, a conditional expectation is usually assumed to
be a projection map onto a sub-algebra. In the paper, a further type of
conditional expectation and an extension of the Lueders - von Neumann
measurement to observables with continuous spectra are considered; both are
defined for a single operator and become a projection map only if they exist
for all operators. Criteria for the existence of the different types of
conditional expectation and of the extension of the Lueders - von Neumann
measurement are presented, and the question whether they coincide is studied.
All this is done in the general framework of Jordan operator algebras. The
examples considered include the type I and type II operator algebras, the
standard Hilbert space model of quantum mechanics, and a no-go result
concerning the conditional expectation of observables that satisfy the
canonical commutator relation.Comment: 10 pages, the original publication is available at
http://www.springerlink.co
Three-slit experiments and quantum nonlocality
An interesting link between two very different physical aspects of quantum
mechanics is revealed; these are the absence of third-order interference and
Tsirelson's bound for the nonlocal correlations. Considering multiple-slit
experiments - not only the traditional configuration with two slits, but also
configurations with three and more slits - Sorkin detected that third-order
(and higher-order) interference is not possible in quantum mechanics. The EPR
experiments show that quantum mechanics involves nonlocal correlations which
are demonstrated in a violation of the Bell or CHSH inequality, but are still
limited by a bound discovered by Tsirelson. It now turns out that Tsirelson's
bound holds in a broad class of probabilistic theories provided that they rule
out third-order interference. A major characteristic of this class is the
existence of a reasonable calculus of conditional probability or, phrased more
physically, of a reasonable model for the quantum measurement process.Comment: 9 pages, no figur
Non-Boolean probabilities and quantum measurement
A non-Boolean extension of the classical probability model is proposed. The
non-Boolean probabilities reproduce typical quantum phenomena. The proposed
model is more general and more abstract, but easier to interpret, than the
quantum mechanical Hilbert space formalism and exhibits a particular phenomenon
(state-independent conditional probabilities) which may provide new
opportunities for an understanding of the quantum measurement process. Examples
of the proposed model are provided, using Jordan operator algebras.Comment: 12 pages, the original publication is available at http://www.iop.or
Acquired equine polyneuropathy of Nordic horses:A conspicuous inclusion body schwannopathy
acceptedVersio