Entangled Mixed States and Local Purification

Linden, Massar and Popescu have recently given an optimization argument to show that a single two-qubit Werner state, or any other mixture of the maximally entangled Bell states, cannot be purified by local operations and classical communications. We generalise their result and give a simple explanation. In particular, we show that no purification scheme using local operations and classical communications can produce a pure singlet from any mixed state of two spin-1/2 particles. More generally, no such scheme can produce a maximally entangled state of any pair of finite-dimensional systems from a generic mixed state. We also show that the Werner states belong to a large class of states whose fidelity cannot be increased by such a scheme.Comment: 3 pages, Latex with Revtex. Small clarifications and reference adde

Limits on the Halo White Dwarf Component of Baryonic Dark Matter from the {\em Hubble Deep Field}

The MACHO collaboration lensing event statistics suggest that a significant fraction of the dark galactic halo can be comprised of baryonic matter in the form of white dwarf stars with masses between 0.1 and 1.0 \Msun . Such a halo white dwarf population, in order to have escaped detection by those who observe the white dwarf luminosity function of the disk, must have formed from an old population. The observations indicate that the number of halo white dwarfs per cubic parsec per unit bolometric magnitude is less than $10^{-5}$ at $10^{-4.5}$\Lsun; the number must rise significantly at lower luminosities to provide the needed baryonic halo mass. Such white dwarfs may easily escape detection in most current and earlier surveys. Though it is limited in angular extent, the {\em Hubble Deep Field} (HDF) probes a sufficient volume of the galactic halo to provide interesting limits on the number of halo white dwarf stars, and on the fraction of the halo mass that they can make up. If the HDF field can be probed for stars down to $V=29.8$ then the MACHO result suggests that there could be up to 12 faint halo white dwarfs visible in the HDF. Finding (or not finding) these stars in turn places interesting constraints on star formation immediately following the formation of the galaxy.Comment: 10 pages, AASTEX, 1 table, no figures, accepted for publication in Ap.J. Letter

The Initial Value Problem For Maximally Non-Local Actions

We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at most discretely enlarged, and may even be restricted, with respect to that of a local theory. We show that the solutions are those of a local theory whose (spacetime constant) parameters vary with the initial value data according to algebraic equations. The various roots of these algebraic equations can be plausibly interpreted in quantum mechanics as different components of a multi-component wave function. It is also possible that the consistency of these algebraic equations imposes constraints upon the initial value data which appear miraculous from the context of a local theory.Comment: 8 pages, LaTeX 2 epsilo

Counterfactual Quantum Cryptography

Quantum cryptography allows one to distribute a secret key between two remote parties using the fundamental principles of quantum mechanics. The well-known established paradigm for the quantum key distribution relies on the actual transmission of signal particle through a quantum channel. This paper shows that the task of a secret key distribution can be accomplished even though a particle carrying secret information is not in fact transmitted through the quantum channel. The proposed protocols can be implemented with current technologies and provide practical security advantages by eliminating the possibility that an eavesdropper can directly access the entire quantum system of each signal particle.Comment: 19 pages, 1 figure; a little ambiguity in the version 1 removed; abstract, text, references, and appendix revised; suggestions and comments are highly appreciate

Some recent applications of XTRAN3S

A time marching finite difference code, XTRAN3S that solves the three dimensional transonic small perturbation equation for flow over isolated wings was developed. During initial applications of the program, problems were encountered in the prediction of unsteady forces. The use of a revised grid and force calculation scheme improved those predictions. Comparisons are made between predicted and experimental pressure data for a rectangular supercritical wing. Comparisons of steady and unsteady data at M sub infinity = 0.700 show good agreement between calculated and experimental values. A comparison of steady data at M sub infinity 0.825 shows poor agreement between calculations and experiment. Program difficulties were encountered with swept and tapered configurations

On Multipartite Pure-State Entanglement

We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the quantification of multipartite pure-state entanglement are discussed. Further, as an application of the techniques used here, we show that any purification of a bipartite PPT bound entangled state is tri-inseparable, i.e. has none of its three bipartite partial traces separable.Comment: 8 Pages ReVTeX, 4 figures (eps); v2: Revised terminology, added two references and other minor changes; v3: Minor changes, added two references, added author's middle initial; v4: One footnote remove

Entanglement Swapping Chains for General Pure States

We consider entanglement swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalised Bell measurements with the result that the two end parties end up sharing a entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain.Comment: 18 pages, 5 figure

A Closed-Form Expression for the Gravitational Radiation Rate from Cosmic Strings

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.Comment: 29 pages TeX, 16 figures and computer C-code available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-10, (section 7 has been expanded, two figures added, and minor grammatical changes made.

Microlens Parallax Asymmetries Toward the LMC

If the microlensing events now being detected toward the Large Magellanic Cloud (LMC) are due to lenses in the Milky Way halo, then the events should typically have asymmetries of order 1% due to parallax from the reflex motion of the Earth. By contrast, if the lenses are in the LMC, the parallax effects should be negligible. A ground-based search for such parallax asymmetries would therefore clarify the location of the lenses. A modest effort (2 hours per night on a 1 m telescope) could measure 15 parallax asymmetries over 5 years and so marginally discriminate between the halo and the LMC as the source of the lenses. A dedicated 1 m telescope would approximately double the number of measurements and would therefore clearly distinguish between the alternatives. However, compared to satellite parallaxes, the information extracted from ground-based parallaxes is substantially less useful for understanding the nature of the halo lenses (if that is what they are). The backgrounds of asymmetries due to binary-source and binary-lens events are estimated to be approximately 7% and 12% respectively. These complicate the interpretation of detected parallax asymmetries, but not critically.Comment: Submitted to ApJ, 17 pages, including 2 embedded figure