709 research outputs found
Physical Logic
In R.D. Sorkin's framework for logic in physics a clear separation is made
between the collection of unasserted propositions about the physical world and
the affirmation or denial of these propositions by the physical world. The
unasserted propositions form a Boolean algebra because they correspond to
subsets of an underlying set of spacetime histories. Physical rules of
inference, apply not to the propositions in themselves but to the affirmation
and denial of these propositions by the actual world. This physical logic may
or may not respect the propositions' underlying Boolean structure. We prove
that this logic is Boolean if and only if the following three axioms hold: (i)
The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied
then its negation, or complement, is affirmed. When a physical system is
governed by a dynamical law in the form of a quantum measure with the rule that
events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid
and need to be modified. One promising scheme for quantum mechanics as quantum
measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is
as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other
minor change
Wigner-Yanase skew information as tests for quantum entanglement
A Bell-type inequality is proposed in terms of Wigner-Yanase skew
information, which is quadratic and involves only one local spin observable at
each site. This inequality presents a hierarchic classification of all states
of multipartite quantum systems from separable to fully entangled states, which
is more powerful than the one presented by quadratic Bell inequalities from
two-entangled to fully entangled states. In particular, it is proved that the
inequality provides an exact test to distinguish entangled from nonentangled
pure states of two qubits. Our inequality sheds considerable light on
relationships between quantum entanglement and information theory.Comment: 5 page
Observation of three-photon Greenberger-Horne-Zeilinger entanglement
We present the experimental observation of polarization entanglement for
three spatially separated photons. Such states of more than two entangled
particles, known as GHZ states, play a crucial role in fundamental tests of
quantum mechanics versus local realism and in many quantum information and
quantum computation schemes. Our experimental arrangement is such that we start
with two pairs of entangled photons and register one photon in a way that any
information as to which pair it belongs to is erased. The registered events at
the detectors for the remaining three photons then exhibit the desired GHZ
correlations.Comment: Revtex, 4 pages, uses floats, epsfi
Gravitation: Global Formulation and Quantum Effects
A nonintegrable phase-factor global approach to gravitation is developed by
using the similarity of teleparallel gravity with electromagnetism. The phase
shifts of both the COW and the gravitational Aharonov-Bohm effects are
obtained. It is then shown, by considering a simple slit experiment, that in
the classical limit the global approach yields the same result as the
gravitational Lorentz force equation of teleparallel gravity. It represents,
therefore, the quantum mechanical version of the classical description provided
by the gravitational Lorentz force equation. As teleparallel gravity can be
formulated independently of the equivalence principle, it will consequently
require no generalization of this principle at the quantum level.Comment: Latex (IOP style), 14 pages, 3 figures. To appear in Classical and
Quantum Gravit
Compositional Heterogeneity of Impact Melt Rocks at the Haughton Impact Structure, Canada: Implications for Planetary Processes and Remote Sensing
Connecting the surface expression of impact craterârelated lithologies to planetary or regional subsurface compositions requires an understanding of material transport during crater formation. Here, we use imaging spectroscopy of six clastârich impact melt rock outcrops within the wellâpreserved 23.5âMa, 23âkm diameter Haughton impact structure, Canada, to determine melt rock composition and spatial heterogeneity. We compare results from outcrop to outcrop, using clasts, groundmass, and integrated clastâgroundmass compositions as tracers of transport during craterâfill melt rock formation and cooling. Supporting laboratory imaging spectroscopy analyses of 91 meltâbearing breccia and clast samples and microscopic Xâray fluorescence elemental mapping of cut samples paired with spectroscopy of identical surfaces validate outcropâscale lithological determinations. Results show different clastârich impact melt rock compositions at three sites kilometers apart and an inverse correlation between silicaârich (sandstone, gneiss, and phyllosilicateârich shales) and gypsumârich rocks that suggests differences in source depth with location. In the target stratigraphy, gypsum is primarily sourced from ~1âkm depth, while gneiss is from >1.8âkm depth, sandstone from >1.3 km, and shales from ~1.6â1.7 km. Observed heterogeneities likely result from different excavation depths coupled with rapid quenching of the melt due to high content of cool clasts. Results provide quantitative constraints for numerical models of impact structure formation and give new details on melt rock heterogeneity important in interpreting mission data and planning sample return of impactites, particularly for bodies with impacts into sedimentary and volatileâbearing targets, e.g., Mars and Ceres
Bell's theorem without inequalities and without probabilities for two observers
A proof of Bell's theorem using two maximally entangled states of two qubits
is presented. It exhibits a similar logical structure to Hardy's argument of
``nonlocality without inequalities''. However, it works for 100% of the runs of
a certain experiment. Therefore, it can also be viewed as a
Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated
regions.Comment: REVTeX, 4 page
Quantum codewords contradict local realism
Quantum codewords are highly entangled combinations of two-state systems. The
standard assumptions of local realism lead to logical contradictions similar to
those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and
Mermin. The new contradictions have some noteworthy features that did not
appear in the older ones.Comment: 9 pages LaTeX, 1 figur
Greenberger-Horne-Zeilinger paradox for continuous variables
We show how to construct states for which a Greenberger-Horne-Zeilinger type
paradox occurs if each party measures either the position or momentum of his
particle. The paradox can be ascribed to the anticommutation of certain
translation operators in phase space. We then rephrase the paradox in terms of
modular and binary variables. The origin of the paradox is then due to the fact
that the associativity of addition of modular variables is true only for
c-numbers but does not hold for operators.Comment: 4 pages, no figure
Proposed direct test of a certain type of noncontextuality in quantum mechanics
The noncontextuality of quantum mechanics can be directly tested by measuring
two entangled particles with more than two outcomes per particle. The two
associated contexts are "interlinked" by common observables.Comment: 9 pages 2 figure
Information Invariance and Quantum Probabilities
We consider probabilistic theories in which the most elementary system, a
two-dimensional system, contains one bit of information. The bit is assumed to
be contained in any complete set of mutually complementary measurements. The
requirement of invariance of the information under a continuous change of the
set of mutually complementary measurements uniquely singles out a measure of
information, which is quadratic in probabilities. The assumption which gives
the same scaling of the number of degrees of freedom with the dimension as in
quantum theory follows essentially from the assumption that all physical states
of a higher dimensional system are those and only those from which one can
post-select physical states of two-dimensional systems. The requirement that no
more than one bit of information (as quantified by the quadratic measure) is
contained in all possible post-selected two-dimensional systems is equivalent
to the positivity of density operator in quantum theory.Comment: 8 pages, 1 figure. This article is dedicated to Pekka Lahti on the
occasion of his 60th birthday. Found. Phys. (2009
- âŠ