Detecting separable states via semidefinite programs

We introduce a new technique to detect separable states using semidefinite programs. This approach provides a sufficient condition for separability of a state that is based on the existence of a certain local linear map applied to a known separable state. When a state is shown to be separable, a proof of this fact is provided in the form of an explicit convex decomposition of the state in terms of product states. All states in the interior of the set of separable states can be detected in this way, except maybe for a set of measure zero. Even though this technique is more suited for a numerical approach, a new analytical criterion for separability can also be derived.Comment: 8 pages, accepted for publication in Physical Review

VSOP observation of the quasar PKS 2215+020: a new laboratory for core-jet physics at z=3.572

We report results of a VSOP (VLBI Space Observatory Programme) observation of a high redshift quasar PKS 2215+020 (z=3.572). The ~1 milliarcsecond resolution image of the quasar reveals a prominent `core-jet' structure on linear scales from 5/h to 300/h pc ($H_0=100*h km/(s*Mpc). The brightness temperatures and sizes of bright features identified in the jet are consistent with emission from relativistic shocks dominated by adiabatic energy losses. The jet is powered by the central black hole with estimated mass of ~4*10^9 solar masses. Comparisons with VLA and ROSAT observations indicate a possible presence of an extended radio/X-ray halo surrounding 2215+020.Comment: 15 pages, 6 figures, aastex macros; accepted for publication in The Astrophysical Journal, V.546, N.2 *(January 10 2001

Low rank positive partial transpose states and their relation to product vectors

It is known that entangled mixed states that are positive under partial transposition (PPT states) must have rank at least four. In a previous paper we presented a classification of rank four entangled PPT states which we believe to be complete. In the present paper we continue our investigations of the low rank entangled PPT states. We use perturbation theory in order to construct rank five entangled PPT states close to the known rank four states, and in order to compute dimensions and study the geometry of surfaces of low rank PPT states. We exploit the close connection between low rank PPT states and product vectors. In particular, we show how to reconstruct a PPT state from a sufficient number of product vectors in its kernel. It may seem surprising that the number of product vectors needed may be smaller than the dimension of the kernel.Comment: 29 pages, 4 figure

An Impacting Descent Probe for Europa and the other Galilean Moons of Jupiter

We present a study of an impacting descent probe that increases the science return of spacecraft orbiting or passing an atmosphere-less planetary body of the solar system, such as the Galilean moons of Jupiter. The descent probe is a carry-on small spacecraft (< 100 kg), to be deployed by the mother spacecraft, that brings itself onto a collisional trajectory with the targeted planetary body in a simple manner. A possible science payload includes instruments for surface imaging, characterisation of the neutral exosphere, and magnetic field and plasma measurement near the target body down to very low-altitudes (~1 km), during the probe's fast (~km/s) descent to the surface until impact. The science goals and the concept of operation are discussed with particular reference to Europa, including options for flying through water plumes and after-impact retrieval of very-low altitude science data. All in all, it is demonstrated how the descent probe has the potential to provide a high science return to a mission at a low extra level of complexity, engineering effort, and risk. This study builds upon earlier studies for a Callisto Descent Probe (CDP) for the former Europa-Jupiter System Mission (EJSM) of ESA and NASA, and extends them with a detailed assessment of a descent probe designed to be an additional science payload for the NASA Europa Mission.Comment: 34 pages, 11 figure

Complete hierarchies of efficient approximations to problems in entanglement theory

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multi-party entanglement, (D) the test whether states are multi-party entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree three or less. We then apply very recently established known methods from the theory of semi-definite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of novel, efficiently decidable sufficient criteria for multi-particle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach.Comment: 14 pages, 3 figures, tiny modifications, version to be published in Physical Review

A relativistic helical jet in the gamma-ray AGN 1156+295

We present the results of a number of high resolution radio observations of the AGN 1156+295. These include multi-epoch and multi-frequency VLBI, VSOP, MERLIN and VLA observations made over a period of 50 months. The 5 GHz MERLIN images trace a straight jet extending to 2 arcsec at P.A. -18 degrees. Extended low brightness emission was detected in the MERLIN observation at 1.6 GHz and the VLA observation at 8.5 GHz with a bend of about 90 degrees at the end of the 2 arcsecond jet. A region of similar diffuse emission is also seen about 2 arcseconds south of the radio core. The VLBI images of the blazar reveal a core-jet structure with an oscillating jet on a milli-arcsecond (mas) scale which aligns with the arcsecond jet at a distance of several tens of milli-arcseconds from the core. This probably indicates that the orientation of the jet structure is close to the line of sight, with the northern jet being relativistically beamed toward us. In this scenario the diffuse emission to the north and south is not beamed and appears symmetrical. For the northern jet at the mas scale, proper motions of 13.7 +/-3.5, 10.6 +/- 2.8, and 11.8 +/- 2.8 c are measured in three distinct components of the jet (q_0=0.5, H_0=65 km /s /Mpc are used through out this paper). Highly polarised emission is detected on VLBI scales in the region in which the jet bends sharply to the north-west. The spectral index distribution of the source shows that the strongest compact component has a flat spectrum, and the extended jet has a steep spectrum. A helical trajectory along the surface of a cone was proposed based on the conservation laws for kinetic energy and momentum to explain the observed phenomena, which is in a good agreement with the observed results on scales of 1 mas to 1 arcsec.Comment: 19 pages with 18 figures. Accepted for publication in the A&

Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio

Asymptotic Freedom for Non-Relativistic Confinement

Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given and explicit examples are given for the case of the harmonic oscillator.Comment: 16 pages, 5 figures, RevTex

New classes of n-copy undistillable quantum states with negative partial transposition

The discovery of entangled quantum states from which one cannot distill pure entanglement constitutes a fundamental recent advance in the field of quantum information. Such bipartite bound-entangled (BE) quantum states \emph{could} fall into two distinct categories: (1) Inseparable states with positive partial transposition (PPT), and (2) States with negative partial transposition (NPT). While the existence of PPT BE states has been confirmed, \emph{only one} class of \emph{conjectured} NPT BE states has been discovered so far. We provide explicit constructions of a variety of multi-copy undistillable NPT states, and conjecture that they constitute families of NPT BE states. For example, we show that for every pure state of Schmidt rank greater than or equal to three, one can construct n-copy undistillable NPT states, for any $n\geq1$. The abundance of such conjectured NPT BE states, we believe, considerably strengthens the notion that being NPT is only a necessary condition for a state to be distillable.Comment: Latex, 10 page