48 research outputs found
A hierarchy of compatibility and comeasurability levels in quantum logics with unique conditional probabilities
In the quantum mechanical Hilbert space formalism, the probabilistic
interpretation is a later ad-hoc add-on, more or less enforced by the
experimental evidence, but not motivated by the mathematical model itself. A
model involving a clear probabilistic interpretation from the very beginning is
provided by the quantum logics with unique conditional probabilities. It
includes the projection lattices in von Neumann algebras and here probability
conditionalization becomes identical with the state transition of the Lueders -
von Neumann measurement process. This motivates the definition of a hierarchy
of five compatibility and comeasurability levels in the abstract setting of the
quantum logics with unique conditional probabilities. Their meanings are: the
absence of quantum interference or influence, the existence of a joint
distribution, simultaneous measurability, and the independence of the final
state after two successive measurements from the sequential order of these two
measurements. A further level means that two elements of the quantum logic
(events) belong to the same Boolean subalgebra. In the general case, the five
compatibility and comeasurability levels appear to differ, but they all
coincide in the common Hilbert space formalism of quantum mechanics, in von
Neumann algebras, and in some other cases.Comment: 12 page
Joint system quantum descriptions arising from local quantumness
Bipartite correlations generated by non-signalling physical systems that
admit a finite-dimensional local quantum description cannot exceed the quantum
limits, i.e., they can always be interpreted as distant measurements of a
bipartite quantum state. Here we consider the effect of dropping the assumption
of finite dimensionality. Remarkably, we find that the same result holds
provided that we relax the tensor structure of space-like separated
measurements to mere commutativity. We argue why an extension of this result to
tensor representations seems unlikely
A topos for algebraic quantum theory
The aim of this paper is to relate algebraic quantum mechanics to topos
theory, so as to construct new foundations for quantum logic and quantum
spaces. Motivated by Bohr's idea that the empirical content of quantum physics
is accessible only through classical physics, we show how a C*-algebra of
observables A induces a topos T(A) in which the amalgamation of all of its
commutative subalgebras comprises a single commutative C*-algebra. According to
the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter
has an internal spectrum S(A) in T(A), which in our approach plays the role of
a quantum phase space of the system. Thus we associate a locale (which is the
topos-theoretical notion of a space and which intrinsically carries the
intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which
is the noncommutative notion of a space). In this setting, states on A become
probability measures (more precisely, valuations) on S(A), and self-adjoint
elements of A define continuous functions (more precisely, locale maps) from
S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to
propositions about the system, the pairing map that assigns a (generalized)
truth value to a state and a proposition assumes an extremely simple
categorical form. Formulated in this way, the quantum theory defined by A is
essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical
Physic
The PHENIX Experiment at RHIC
The physics emphases of the PHENIX collaboration and the design and current
status of the PHENIX detector are discussed. The plan of the collaboration for
making the most effective use of the available luminosity in the first years of
RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program
available at http://www.rhic.bnl.gov/phenix
Genome-wide association meta-analysis of corneal curvature identifies novel loci and shared genetic influences across axial length and refractive error.
Corneal curvature, a highly heritable trait, is a key clinical endophenotype for myopia - a major cause of visual impairment and blindness in the world. Here we present a trans-ethnic meta-analysis of corneal curvature GWAS in 44,042 individuals of Caucasian and Asian with replication in 88,218 UK Biobank data. We identified 47 loci (of which 26 are novel), with population-specific signals as well as shared signals across ethnicities. Some identified variants showed precise scaling in corneal curvature and eye elongation (i.e. axial length) to maintain eyes in emmetropia (i.e. HDAC11/FBLN2 rs2630445, RBP3 rs11204213); others exhibited association with myopia with little pleiotropic effects on eye elongation. Implicated genes are involved in extracellular matrix organization, developmental process for body and eye, connective tissue cartilage and glycosylation protein activities. Our study provides insights into population-specific novel genes for corneal curvature, and their pleiotropic effect in regulating eye size or conferring susceptibility to myopia