Atemporal diagrams for quantum circuits

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using PSTrick

The Nature and Location of Quantum Information

Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other arguments show that the infinite amount of information needed to specify a precise vector in its Hilbert space is not a measure of the information carried by a quantum entity with a $d$-dimensional Hilbert space; the latter is, instead, bounded by log d bits (1 bit per qubit). The two bits of information transmitted in dense coding are located not in one but in the correlation between two qubits, consistent with this bound. A quantum channel can be thought of as a "structure" or collection of frameworks, and the physical location of the information in the individual frameworks can be used to identify the location of the channel. Analysis of a quantum circuit used as a model of teleportation shows that the location of the channel depends upon which structure is employed; for ordinary teleportation it is not (contrary to Deutsch and Hayden) present in the two bits resulting from the Bell-basis measurement, but in correlations of these with a distant qubit. In neither teleportation nor dense coding does information travel backwards in time, nor is it transmitted by nonlocal (superluminal) influences. It is (tentatively) proposed that all aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.Comment: Latex 29 pages, uses PSTricks for figure

Phase Structure of 2-Flavor Quark Matter: Heterogeneous Superconductors

We analyze the free energy of charge and color neutral 2-flavor quark matter within the BCS approximation. We consider both the homogeneous gapless superconducting phase and the heterogeneous mixed phase where normal and BCS superconducting phases coexist. We calculate the surface tension between normal and superconducting phases and use it to compare the free energies of the gapless and mixed phases. Our calculation, which retains only the leading order gradient contribution to the free energy, indicates that the mixed phase is energetically favored over an interesting range of densities of relevance to 2 flavor quark matter in neutron stars.Comment: 11 pages, 4 figures. Major Revisions. Includes a detailed discussion of the kinetic terms of the effective theory, instabilities of the gapless phase and the charge neutral phase diagra

Weak Lensing Determination of the Mass in Galaxy Halos

We detect the weak gravitational lensing distortion of 450,000 background galaxies (20<R<23) by 790 foreground galaxies (R<18) selected from the Las Campanas Redshift Survey (LCRS). This is the first detection of weak lensing by field galaxies of known redshift, and as such permits us to reconstruct the shear profile of the typical field galaxy halo in absolute physical units (modulo H_0), and to investigate the dependence of halo mass upon galaxy luminosity. This is also the first galaxy-galaxy lensing study for which the calibration errors are negligible. Within a projected radius of 200 \hkpc, the shear profile is consistent with an isothermal profile with circular velocity 164+-20 km/s for an L* galaxy, consistent with typical disk rotation at this luminosity. This halo mass normalization, combined with the halo profile derived by Fischer et al (2000) from lensing analysis SDSS data, places a lower limit of (2.7+-0.6) x 10^{12}h^{-1} solar masses on the mass of an L* galaxy halo, in good agreement with satellite galaxy studies. Given the known luminosity function of LCRS galaxies, and the assumption that $M\propto L^\beta$ for galaxies, we determine that the mass within 260\hkpc of normal galaxies contributes $\Omega=0.16\pm0.03$ to the density of the Universe (for $\beta=1$) or $\Omega=0.24\pm0.06$ for $\beta=0.5$. These lensing data suggest that $0.6<\beta<2.4$ (95% CL), only marginally in agreement with the usual $\beta\approx0.5$ Faber-Jackson or Tully-Fisher scaling. This is the most complete direct inventory of the matter content of the Universe to date.Comment: 18 pages, incl. 3 figures. Submitted to ApJ 6/7/00, still no response from the referee after four months

Complex X-ray spectral variability in Mkn 421 observed with XMM-Newton

The bright blazar Mkn 421 has been observed four times for uninterrupted durations of ~ 9 - 13 hr during the performance verification and calibration phases of the XMM-Newton mission. The source was strongly variable in all epochs, with variability amplitudes that generally increased to higher energy bands. Although the detailed relationship between soft (0.1 - 0.75 keV) and hard (2 - 10 keV) band differed from one epoch to the next, in no case was there any evidence for a measurable interband lag, with robust upper limits of $| \tau | < 0.08$ hr in the best-correlated light curves. This is in conflict with previous claims of both hard and soft lags of ~1 hr in this and other blazars. However, previous observations suffered a repeated 1.6 hr feature induced by the low-Earth orbital period, a feature that is not present in the uninterrupted XMM-Newton data. The new upper limit on $|\tau|$ leads to a lower limit on the magnetic field strength and Doppler factor of B \delta^{1/3} \gs 4.7 G, mildly out of line with the predictions from a variety of homogeneous synchrotron self-Compton emission models in the literature of $B \delta^{1/3} = 0.2 - 0.8$ G. Time-dependent spectral fitting was performed on all epochs, and no detectable spectral hysteresis was seen. We note however that the source exhibited significantly different spectral evolutionary behavior from one epoch to the next, with the strongest correlations in the first and last and an actual divergance between soft and hard X-ray bands in the third. This indicates that the range of spectral variability behavior in Mkn 421 is not fully described in these short snippets; significantly longer uninterrupted light curves are required, and can be obtained with XMM-Newton.Comment: 21 pages, 4 figures, accepted for ApJ, scheduled for August 1, 200

Consistent Resolution of Some Relativistic Quantum Paradoxes

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of Einstein-Podolsky-Rosen, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.Comment: Latex 42 pages, 7 figures in text using PSTrick

The introduction of an holistic design approach through a teaching company scheme

Traditional design approaches separate the various functions of design such as material selection, performance modelling and tolerance specification into discrete entities. Whilst this allows more focused methods to be used at each stage, areas of conflict or benefit may be overlooked, and the designer is left to bring the loose ends together. This paper looks at a synthesis approach that draws upon a number of current design themes. The design process is considered along with various aspects such as product development, design-for-`X' methodologies and material selection. The need for the preservation of design knowledge and reasoning, the so called wh-? questions, within the process are considered along with various models of the design process. The paper draws these various aspects together to form a more holistic approach to design. The application of this technique within the Teaching Company Scheme is briefly discussed

Polarized Diffuse Emission at 2.3 GHz in a High Galactic Latitude Area

Polarized diffuse emission observations at 2.3 GHz in a high Galactic latitude area are presented. The 2\degr X 2\degr field, centred in (\alpha=5^h,\delta=-49\degr), is located in the region observed by the BOOMERanG experiment. Our observations has been carried out with the Parkes Radio telescope and represent the highest frequency detection done to date in low emission areas. Because of a weaker Faraday rotation action, the high frequency allows an estimate of the Galactic synchrotron contamination of the Cosmic Microwave Background Polarization (CMBP) that is more reliable than that done at 1.4 GHz. We find that the angular power spectra of the E- and B-modes have slopes of \beta_E = -1.46 +/- 0.14 and \beta_B = -1.87 +/- 0.22, indicating a flattening with respect to 1.4 GHz. Extrapolated up to 32 GHz, the E-mode spectrum is about 3 orders of magnitude lower than that of the CMBP, allowing a clean detection even at this frequency. The best improvement concerns the B-mode, for which our single-dish observations provide the first estimate of the contamination on angular scales close to the CMBP peak (about 2 degrees). We find that the CMBP B-mode should be stronger than synchrotron contamination at 90 GHz for models with T/S > 0.01. This low level could move down to 60-70 GHz the optimal window for CMBP measures.Comment: 5 pages, 6 figures, accepted for publication in MNRAS Letter