Loophole-free Bell test based on local precertification of photon's presence

A loophole-free violation of Bell inequalities is of fundamental importance for demonstrating quantum nonlocality and long-distance device-independent secure communication. However, transmission losses represent a fundamental limitation for photonic loophole-free Bell tests. A local precertification of the presence of the photons immediately before the local measurements may solve this problem. We show that local precertification is feasible by integrating three current technologies: (i) enhanced single-photon down-conversion to locally create a flag photon, (ii) nanowire-based superconducting single-photon detectors for a fast flag detection, and (iii) superconducting transition-edge sensors to close the detection loophole. We carry out a precise space-time analysis of the proposed scheme, showing its viability and feasibility.Comment: REVTeX4, 7 Pages, 1 figur

On the size of approximately convex sets in normed spaces

Let X be a normed space. A subset A of X is approximately convex if $d(ta+(1-t)b,A) \le 1$ for all $a,b \in A$ and $t \in [0,1]$ where $d(x,A)$ is the distance of $x$ to $A$. Let \Co(A) be the convex hull and \diam(A) the diameter of $A$. We prove that every $n$-dimensional normed space contains approximately convex sets $A$ with \mathcal{H}(A,\Co(A))\ge \log_2n-1 and \diam(A) \le C\sqrt n(\ln n)^2, where $\mathcal{H}$ denotes the Hausdorff distance. These estimates are reasonably sharp. For every $D>0$, we construct worst possible approximately convex sets in $C[0,1]$ such that \mathcal{H}(A,\Co(A))=\diam(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.Comment: 32 pages. See also http://www.math.sc.edu/~howard

Extremal Approximately Convex Functions and Estimating the Size of Convex Hulls

A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$f((x+y)/2) \le (f(x)+f(y))/2 + 1.$$ A thorough study of approximately convex functions is made. The principal results are a sharp universal upper bound for lower semi-continuous approximately convex functions that vanish on the vertices of a simplex and an explicit description of the unique largest bounded approximately convex function~$E$ vanishing on the vertices of a simplex. A set $A$ in a normed space is an approximately convex set iff for all $a,b\in A$ the distance of the midpoint $(a+b)/2$ to $A$ is $\le 1$. The bounds on approximately convex functions are used to show that in $\R^n$ with the Euclidean norm, for any approximately convex set $A$, any point $z$ of the convex hull of $A$ is at a distance of at most $[\log_2(n-1)]+1+(n-1)/2^{[\log_2(n-1)]}$ from $A$. Examples are given to show this is the sharp bound. Bounds for general norms on $R^n$ are also given.Comment: 39 pages. See also http://www.math.sc.edu/~howard

The Centaurus A Northern Middle Lobe as a Buoyant Bubble

We model the northern middle radio lobe of Centaurus A (NGC 5128) as a buoyant bubble of plasma deposited by an intermittently active jet. The extent of the rise of the bubble and its morphology imply that the ratio of its density to that of the surrounding ISM is less than 10^{-2}, consistent with our knowledge of extragalactic jets and minimal entrainment into the precursor radio lobe. Using the morphology of the lobe to date the beginning of its rise through the atmosphere of Centaurus A, we conclude that the bubble has been rising for approximately 140Myr. This time scale is consistent with that proposed by Quillen et al. (1993) for the settling of post-merger gas into the presently observed large scale disk in NGC 5128, suggesting a strong connection between the delayed re-establishment of radio emission and the merger of NGC 5128 with a small gas-rich galaxy. This suggests a connection, for radio galaxies in general, between mergers and the delayed onset of radio emission. In our model, the elongated X-ray emission region discovered by Feigelson et al. (1981), part of which coincides with the northern middle lobe, is thermal gas that originates from the ISM below the bubble and that has been uplifted and compressed. The "large-scale jet" appearing in the radio images of Morganti et al. (1999) may be the result of the same pressure gradients that cause the uplift of the thermal gas, acting on much lighter plasma, or may represent a jet that did not turn off completely when the northern middle lobe started to buoyantly rise. We propose that the adjacent emission line knots (the "outer filaments") and star-forming regions result from the disturbance, in particular the thermal trunk, caused by the bubble moving through the extended atmosphere of NGC 5128.Comment: 38 pages, 13 figures, submitted to ApJ; a version with higher resolution figures is available at http://www.mso.anu.edu.au/~saxton/papers/cena.pd

Profiling of oligolignols reveals monolignol coupling conditions in lignifying poplar xylem

Lignin is an aromatic heteropolymer, abundantly present in the walls of secondary thickened cells. Although much research has been devoted to the structure and composition of the polymer to obtain insight into lignin polymerization, the low-molecular weight oligolignol fraction has escaped a detailed characterization. This fraction, in contrast to the rather inaccessible polymer, is a simple and accessible model that reveals details about the coupling of monolignols, an issue that has raised considerable controversy over the past years. We have profiled the methanol-soluble oligolignol fraction of poplar (Populus spp.) xylem, a tissue with extensive lignification. Using liquid chromatography-mass spectrometry, chemical synthesis, and nuclear magnetic resonance, we have elucidated the structures of 38 compounds, most of which were dimers, trimers, and tetramers derived from coniferyl alcohol, sinapyl alcohol, their aldehyde analogs, or vanillin. All structures support the recently challenged random chemical coupling hypothesis for lignin polymerization. Importantly, the structures of two oligomers, each containing a γ-p-hydroxybenzoylated syringyl unit, strongly suggest that sinapyl p-hydroxybenzoate is an authentic precursor for lignin polymerization in poplar

Quantum computation with optical coherent states

We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements and "small" coherent superposition resource states

Interactions of Jets with Inhomogeneous Cloudy Media

We present two-dimensional slab-jet simulations of jets in inhomogeneous media consisting of a tenuous hot medium populated with a small filling factor by warm, dense clouds. The simulations are relevant to the structure and dynamics of sources such as Gigahertz Peak Spectrum and Compact Steep Spectrum radio galaxies, High Redshift Radio Galaxies and radio galaxies in cooling flows. The jets are disrupted to a degree depending upon the filling factor of the clouds. With a small filling factor, the jet retains some forward momentum but also forms a halo or bubble around the source. At larger filling factors channels are formed in the cloud distribution through which the jet plasma flows and a hierarchical structure consisting of nested lobes and an outer enclosing bubble results. We suggest that the CSS quasar 3C48 is an example of a low filling factor jet - interstellar medium interaction whilst M87 may be an example of the higher filling factor type of interaction. Jet disruption occurs primarily as a result of Kelvin-Helmholtz instabilities driven by turbulence in the radio cocoon not through direct jet-cloud interactions, although there are some examples of these. In all radio galaxies whose morphology may be the result of jet interactions with an inhomogeneous interstellar medium we expect that the dense clouds will be optically observable as a result of radiative shocks driven by the pressure of the radio cocoon. We also expect that the radio galaxies will possess faint haloes of radio emitting material well beyond the observable jet structure.Comment: 21 pages, 16 figures, submitted to MNRAS. A version with full resolution figures is available at: http://www.mssl.ucl.ac.uk/~cjs2/pdf/cloudy_hue.pd

Transfer of Nonclassical Properties from A Microscopic Superposition to Macroscopic Thermal States in The High Temperature Limit

We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.Comment: minor corrections, acknowledgments added, Phys.Rev.Lett., in pres