Bell's theorem without inequalities and without unspeakable information

A proof of Bell's theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.Comment: REVTeX4, 4 pages, 1 figure; for Asher Peres' Festschrift, to be published in Found. Phy

Decoherence-Free Quantum Information Processing with Four-Photon Entangled States

Decoherence-free states protect quantum information from collective noise, the predominant cause of decoherence in current implementations of quantum communication and computation. Here we demonstrate that spontaneous parametric down-conversion can be used to generate four-photon states which enable the encoding of one qubit in a decoherence-free subspace. The immunity against noise is verified by quantum state tomography of the encoded qubit. We show that particular states of the encoded qubit can be distinguished by local measurements on the four photons only.Comment: 4 pages, 4 eps figures, revtex

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

Multi-level, multi-party singlets as ground states and their role in entanglement distribution

We show that a singlet of many multi-level quantum systems arises naturally as the ground state of a physically-motivated Hamiltonian. The Hamiltonian simply exchanges the states of nearest-neighbours in some network of qudits (d-level systems); the results are independent of the strength of the couplings or the network's topology. We show that local measurements on some of these qudits project the unmeasured qudits onto a smaller singlet, regardless of the choice of measurement basis at each measurement. It follows that the entanglement is highly persistent, and that through local measurements, a large amount of entanglement may be established between spatially-separated parties for subsequent use in distributed quantum computation.Comment: Corrected method for physical preparatio

Semicentral idempotents in the multiplication ring of a centrally closed prime ring

Let R be a ring and let M(R) stand for the multiplication ring of R. An idempotent E in M(R) is called left semicentral if its range E(R) is a right ideal of R. In the case that R is prime and centrally closed we give a description of the left semicentral idempotents in M(R). As an application we prove that, if, in addition, M(R) is Baer (respectively, regular or Rickart), then R is Baer (respectively, regular or Rickart). Similar results for *-rings are also proved.• Ministerio de Ciencia, Innovación y Universidades de España y Fondos FEDER: Proyecto MTM2009-12067 • Junta de Andalucía: Proyecto FQM290peerReviewe

Proposed experiment for the quantum "Guess my number" protocol

An experimental realization of the entanglement-assisted "Guess my number" protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency eta > 0.70, which would require single photon detectors of efficiency sigma > 0.89. We propose a modification of the protocol which can be translated into a real experiment using present-day technology. In the proposed experiment, the quantum reduction of the multi-party communication complexity would require an efficiency eta > 0.05, achievable with detectors of sigma > 0.47, for four parties, and eta > 0.17 (sigma > 0.55) for three parties.Comment: REVTeX4, 4 pages, 1 figur

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations

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

Phylogenetic analysis of the pearlfish tribe Carapini (Pisces: Carapidae)

Fishes of the tribe Carapini (Encheliophis and Carapus) share a noteworthy peculiarity: they shelter in holothurian echinoderms or bivalve hosts. Some species are considered parasitic, others commensal. This study focuses on the phylogeny of the tribe, using two other Carapidae species as an outgroup (Snyderidia canina and Onuxodon fowleri). Insofar as possible, the selected anatomical and behavioural characters where chosen in an ecomorphological perspective, as features that could be responses to various lifestyle-related constraints. Our character selection also took into account the fact that some features are (presumably) linked. Such features were grouped together as a single trait to avoid their overvaluation.This methodology enabled commensals to be separated from parasites, the former belonging to Carapus and the latter to Encheliophis. Carapus species reflect in their morphology the constraints imposed by a diet of hard, mobile, elusive prey, showing predator-type features: a strong dentition, a wide mouth opening, a robust food intake apparatus. On the other hand, the endoparasitic Encheliophis species show a generally weaker buccal apparatus and narrow mouth opening, in relation to the different constraints of their lifestyle where the diet constraints are less pronounced: they eat body parts of their host. Changes in both generic diagnoses are proposed and three species are transferred from Encheliophis to Carapus

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