It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of EPR-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good
feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loophole of course), for a given number $n$ of measurement settings. We allow for arbitrary measurement directions, and arbitrary weightings of the outcomes in the EPR-steering inequality. This is a difficult optimization problem for large $n$, so we also consider more practical ways of constructing near-optimal EPR-steering inequalities in this limit.
We present models for the X-ray spectrum of the Seyfert 2 galaxy NGC 1068. These are fitted to data obtained using the High Energy Transmission Grating (HETG) on the Chandra X-ray observatory. The data show line and radiative recombination continuum
(RRC) emission from a broad range of ions and elements. The models explore the importance of excitation processes for these lines including photoionization followed by recombination, radiative excitation by absorption of continuum radiation and inner shell fluorescence. The models show that the relative importance of these processes depends on the conditions in the emitting gas, and that no single emitting component can fit the entire spectrum. In particular, the relative importance of radiative excitation and photoionization/recombination differs according to the element and ion stage emitting the line. This in turn implies a diversity of values for the ionization parameter of the various components of gas responsible for the emission, ranging from log(xi)=1 -- 3. Using this, we obtain an estimate for the total amount of gas responsible for the observed emission. The mass flux through the region included in the HETG extraction region is approximately 0.3 Msun/yr assuming ordered flow at the speed characterizing the line widths. This can be compared with what is known about this object from other techniques.
We investigate the transfinite game values arising in infinite chess, providing both upper and lower bounds on the supremum of these values---the omega one of chess---with two senses depending on whether one considers only finite positions or also po
sitions with infinitely many pieces. For lower bounds, we present specific infinite positions with transfinite game values of omega, omega^2, omega^2 times k, and omega^3. By embedding trees into chess, we show that there is a computable infinite chess position that is a win for white if the players are required to play according to a deterministic computable strategy, but which is a draw without that restriction. Finally, we prove that every countable ordinal arises as the game value of a position in infinite three-dimensional chess, and consequently the omega one of infinite three-dimensional chess is as large as it can be, namely, true omega one.
Demonstrating nonclassical effects over longer and longer distances is essential for both quantum technology and fundamental science. The main challenge is loss of photons during propagation, because considering only those cases where photons are det
ected opens a detection loophole in security whenever parties or devices are untrusted. Einstein-Podolsky-Rosen (EPR) steering is equivalent to an entanglement-verification task in which one party (device) is untrusted. We derive arbitrarily loss-tolerant tests, enabling us to perform a detection-loophole-free demonstration of EPR-steering with parties separated by a coiled 1 km optical fiber, with a total loss of 8.9 dB (87%).
We present results from an 87-ks Suzaku observation of the canonical low-excitation radio galaxy (LERG) NGC 6251. We have previously suggested that LERGs violate conventional AGN unification schemes: they may lack an obscuring torus and are likely to
accrete in a radiatively inefficient manner, with almost all of the energy released by the accretion process being channeled into powerful jets. We model the 0.5-20 keV Suzaku spectrum with a single power law of photon index $Gamma=1.82^{+0.04}_{-0.05}$, together with two collisionally ionized plasma models whose parameters are consistent with the known galaxy- and group-scale thermal emission. Our observations confirm that there are no signatures of obscured, accretion-related X-ray emission in NGC 6251, and we show that the luminosity of any such component must be substantially sub-Eddington in nature.
We present results from Suzaku and Swift observations of the nearby radio galaxy 3C 33, and investigate the nature of absorption, reflection, and jet production in this source. We model the 0.5-100 keV nuclear continuum with a power law that is trans
mitted either through one or more layers of pc-scale neutral material, or through a modestly ionized pc-scale obscurer. The standard signatures of reflection from a neutral accretion disk are absent in 3C 33: there is no evidence of a relativistically blurred Fe K$alpha$ emission line, and no Compton reflection hump above 10 keV. We find the upper limit to the neutral reflection fraction is R<0.41 for an e-folding energy of 1 GeV. We observe a narrow, neutral Fe K$alpha$ line, which is likely to originate at least 2,000 R_s from the black hole. We show that the weakness of reflection features in 3C 33 is consistent with two interpretations: either the inner accretion flow is highly ionized, or the black-hole spin configuration is retrograde with respect to the accreting material.
We present results from Chandra and XMM-Newton spectroscopic observations of the nuclei of z<0.5 radio galaxies and quasars from the 3CRR catalog, and examine in detail the dichotomy in the properties of low- and high-excitation radio galaxies. The X
-ray spectra of low-excitation sources (those with weak or absent optical emission lines) are dominated by unabsorbed emission from a parsec-scale jet, with no contribution from accretion-related emission. These sources show no evidence for an obscuring torus, and are likely to accrete in a radiatively inefficient manner. High-excitation sources (those with prominent optical emission lines), on the other hand, show a significant contribution from a radiatively efficient accretion disk, which is heavily absorbed in the X-ray when they are oriented close to edge-on with respect to the observer. However, the low-excitation/high-excitation division does not correspond to the FRI/FRII division: thus the Fanaroff-Riley dichotomy remains a consequence of the interaction between the jet and the hot-gas environment through which it propagates. Finally, we suggest that accretion of the hot phase of the IGM is sufficient to power all low-excitation radio sources, while high-excitation sources require an additional contribution from cold gas that in turn forms the cold disk and torus. This model explains a number of properties of the radio-loud active galaxy population, and has important implications for AGN feedback mechanisms.
