Deterministic dense coding and entanglement entropy

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of non-maximally entangled qudits in pure state |S>. Our results include the following: (i) We prove that it is possible for a state |S> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d = 3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d + j messages, j = 2, ..., d-1; moreover, we show that the j=2 and j= d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |S> allows the sending of K messages and has the square roof of c as its largest Schmidt coefficient, we show that the inequality c <= d/K, established by Wu et al. [ Phys. Rev. A 73, 042311 (2006)], must actually take the form c < d/K if K = d+1, while our constructions of local unitaries show that equality can be realized if K = d+2 or K = 2d-1.Comment: 19 pages, 2 figures. Published versio

Inconsistency in 9 mm bullets : correlation of jacket thickness to post-impact geometry measured with non-destructive X-ray computed tomography

Fundamental to any ballistic armour standard is the reference projectile to be defeated. Typically, for certification purposes, a consistent and symmetrical bullet geometry is assumed, however variations in bullet jacket dimensions can have far reaching consequences. Traditionally, characteristics and internal dimensions have been analysed by physically sectioning bullets – an approach which is of restricted scope and which precludes subsequent ballistic assessment. The use of a non-destructive X-ray computed tomography (CT) method has been demonstrated and validated Kumar et al., 2011); the authors now apply this technique to correlate bullet impact response with jacket thickness variations. A set of 20 bullets (9 mm DM11) were selected for comparison and an image-based analysis method was employed to map jacket thickness and determine the centre of gravity of each specimen. Both intra- and inter-bullet variations were investigated, with thickness variations of the order of 200 um commonly found along the length of all bullets and angular variations of up to 50 um in some. The bullets were subsequently impacted against a rigid flat plate under controlled conditions (observed on a high-speed video camera) and the resulting deformed projectiles were re-analysed. The results of the experiments demonstrate a marked difference in ballistic performance between bullets from different manufacturers and an asymmetric thinning of the jacket is observed in regions of pre-impact weakness. The conclusions are relevant for future soft armour standards and provide important quantitative data for numerical model correlation and development. The implications of the findings of the work on the reliability and repeatability of the industry standard V50 ballistic test are also discussed

The Construction of Sorkin Triangulations

Some time ago, Sorkin (1975) reported investigations of the time evolution and initial value problems in Regge calculus, for one triangulation each of the manifolds $R*S^3$ and $R^4$. Here we display the simple, local characteristic of those triangulations which underlies the structure found by Sorkin, and emphasise its general applicability, and therefore the general validity of Sorkin's conclusions. We also make some elementary observations on the resulting structure of the time evolution and initial value problems in Regge calculus, and add some comments and speculations.Comment: 5 pages (plus one figure not included, available from author on request), Plain Tex, no local preprint number (Only change: omitted "\magnification" command now replaced

Phases of granular segregation in a binary mixture

We present results from an extensive experimental investigation into granular segregation of a shallow binary mixture in which particles are driven by frictional interactions with the surface of a vibrating horizontal tray. Three distinct phases of the mixture are established viz; binary gas (unsegregated), segregation liquid and segregation crystal. Their ranges of existence are mapped out as a function of the system's primary control parameters using a number of measures based on Voronoi tessellation. We study the associated transitions and show that segregation can be suppressed is the total filling fraction of the granular layer, $C$, is decreased below a critical value, $C_{c}$, or if the dimensionless acceleration of the driving, $\gamma$, is increased above a value $\gamma_{c}$.Comment: 12 pages, 12 figures, submitted to Phys. Rev.

Progress in Lunar Laser Ranging Tests of Relativistic Gravity

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the Equivalence Principle (EP); they also enable several very accurate tests of relativistic gravity. We report the results of our recent analysis of Lunar Laser Ranging (LLR) data giving an EP test of \Delta (M_G/M_I)_{EP} =(-1.0 +/- 1.4) x 10^{-13}. This result yields a Strong Equivalence Principle (SEP) test of \Delta (M_G/M_I)_{SEP} =(-2.0 +/- 2.0) x 10^{-13}. Also, the corresponding SEP violation parameter \eta is (4.4 +/- 4.5) x 10^{-4}, where \eta=4\beta-\gamma-3 and both \beta and \gamma are parametrized post-Newtonian (PPN) parameters. Using the recent Cassini result for the parameter \gamma, PPN parameter \beta is determined to be \beta-1=(1.2 +/- 1.1) x 10^{-4}. The geodetic precession test, expressed as a relative deviation from general relativity, is K_{gp}=-0.0019 +/- 0.0064. The search for a time variation in the gravitational constant results in \dot G/G=(4 +/- 9) x 10^{-13} yr^{-1}, consequently there is no evidence for local (~1AU) scale expansion of the solar system.Comment: 4 pages, revtex4, minor changes made for publicatio

Muon spin rotation/relaxation measurements of the non-centrosymmetric superconductor Mg10Ir19B16

We have searched for time-reversal symmetry breaking fields in the non-centrosymmetric superconductor Mg$_{10}$Ir$_{19}$B$_{16}$ via muon spin relaxation in zero applied field, and we measured the temperature dependence of the superfluid density by muon spin rotation in transverse field to investigate the superconducting pairing symmetry in two polycrystalline samples of signficantly different purities. In the high purity sample, we detected no time-reversal symmetry breaking fields greater than 0.05 G. The superfluid density was also found to be exponentially-flat as T$\to$0, and so can be fit to a single-gap BCS model. In contrast, the lower purity sample showed an increase in the zero-field $\mu$SR relaxation rate below T$_c$ corresponding to a characteristic field strength of 0.6 G. While the temperature-dependence of the superfluid density was also found to be consistent with a single-gap BCS model, the magnitude as T$\to$0 was found to be much lower for a given applied field than in the case of the high purity sample. These findings suggest that the dominant pairing symmetry in high quality Mg$_{10}$Ir$_{19}$B$_{16}$ samples corresponds to the spin-singlet channel, while sample quality drastically affects the superconducting properties of this system.Comment: 6 pages, 5 figures, revised version resubmitted to PR