206 research outputs found
Pentagrams and paradoxes
Klyachko and coworkers consider an orthogonality graph in the form of a
pentagram, and in this way derive a Kochen-Specker inequality for spin 1
systems. In some low-dimensional situations Hilbert spaces are naturally
organised, by a magical choice of basis, into SO(N) orbits. Combining these
ideas some very elegant results emerge. We give a careful discussion of the
pentagram operator, and then show how the pentagram underlies a number of other
quantum "paradoxes", such as that of Hardy.Comment: 14 pages, 4 figure
Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
The set of 60 real rays in four dimensions derived from the vertices of a
600-cell is shown to possess numerous subsets of rays and bases that provide
basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a
basis-critical proof is one that fails if even a single basis is deleted from
it). The proofs vary considerably in size, with the smallest having 26 rays and
13 bases and the largest 60 rays and 41 bases. There are at least 90 basic
types of proofs, with each coming in a number of geometrically distinct
varieties. The replicas of all the proofs under the symmetries of the 600-cell
yield a total of almost a hundred million parity proofs of the BKS theorem. The
proofs are all very transparent and take no more than simple counting to
verify. A few of the proofs are exhibited, both in tabular form as well as in
the form of MMP hypergraphs that assist in their visualization. A survey of the
proofs is given, simple procedures for generating some of them are described
and their applications are discussed. It is shown that all four-dimensional
parity proofs of the BKS theorem can be turned into experimental disproofs of
noncontextuality.Comment: 19 pages, 11 tables, 3 figures. Email address of first author has
been corrected. Ref.[5] has been corrected, as has an error in Fig.3.
Formatting error in Sec.4 has been corrected and the placement of tables and
figures has been improved. A new paragraph has been added to Sec.4 and
another new paragraph to the end of the Appendi
State-independent quantum violation of noncontextuality in four dimensional space using five observables and two settings
Recently, a striking experimental demonstration [G. Kirchmair \emph{et al.},
Nature, \textbf{460}, 494(2009)] of the state-independent quantum mechanical
violation of non-contextual realist models has been reported for any two-qubit
state using suitable choices of \emph{nine} product observables and \emph{six}
different measurement setups. In this report, a considerable simplification of
such a demonstration is achieved by formulating a scheme that requires only
\emph{five} product observables and \emph{two} different measurement setups. It
is also pointed out that the relevant empirical data already available in the
experiment by Kirchmair \emph{et al.} corroborate the violation of the NCR
models in accordance with our proof
Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
A diagrammatic representation is given of the 24 rays of Peres that makes it
easy to pick out all the 512 parity proofs of the Kochen-Specker theorem
contained in them. The origin of this representation in the four-dimensional
geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added.
Minor typos have been correcte
Quantum mechanical effect of path-polarization contextuality for a single photon
Using measurements pertaining to a suitable Mach-Zehnder(MZ) type setup, a
curious quantum mechanical effect of contextuality between the path and the
polarization degrees of freedom of a polarized photon is demonstrated, without
using any notion of realism or hidden variables - an effect that holds good for
the product as well as the entangled states. This form of experimental
context-dependence is manifested in a way such that at \emph{either} of the two
exit channels of the MZ setup used, the empirically verifiable
\emph{subensemble} statistical properties obtained by an arbitrary polarization
measurement depend upon the choice of a commuting(comeasurable) path
observable, while this effect disappears for the \emph{whole ensemble} of
photons emerging from the two exit channels of the MZ setup.Comment: To be published in IJT
On the Black-Hole/Qubit Correspondence
The entanglement classification of four qubits is related to the extremal
black holes of the 4-dimensional STU model via a time-like reduction to three
dimensions. This correspondence is generalised to the entanglement
classification of a very special four-way entanglement of eight qubits and the
black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2
supergravity theories.Comment: 32 pages, very minor changes at the start of Sec. 4.1. Version to
appear in The European Physical Journal - Plu
A Stochastic Description of Dictyostelium Chemotaxis
Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells
Testing foundations of quantum mechanics with photons
The foundational ideas of quantum mechanics continue to give rise to
counterintuitive theories and physical effects that are in conflict with a
classical description of Nature. Experiments with light at the single photon
level have historically been at the forefront of tests of fundamental quantum
theory and new developments in photonics engineering continue to enable new
experiments. Here we review recent photonic experiments to test two
foundational themes in quantum mechanics: wave-particle duality, central to
recent complementarity and delayed-choice experiments; and Bell nonlocality
where recent theoretical and technological advances have allowed all
controversial loopholes to be separately addressed in different photonics
experiments.Comment: 10 pages, 5 figures, published as a Nature Physics Insight review
articl
Intraocular lenses in age-related macular degeneration
Purpose:
The aim of this work is to review the lenses, assessing their advantages and disadvantages. We describe a total of seven types of intraocular lenses (IOLs) recommended for age-related macular degeneration (AMD).
Methods:
We used the PubMed web platform to search for implantable devices in various stages of AMD. We searched for both prospective and retrospective studies and also case reports.
Results:
Clinical results in AMD patients have been described for a total of seven types of IOLs recommended for AMD: an implantable miniature telescope (IMT), IOL-VIP System, Lipshitz macular implant (LMI), sulcus-implanted Lipshitz macular implant, LMI-SI, Fresnel Prism Intraocular Lens, iolAMD and Scharioth Macula Lens.
Conclusions:
We conclude that to objectively ascertain the effectiveness and safety of these lenses, further independent clinical studies with longer follow-up data are necessary prior to the general use of these optical devices
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