94 research outputs found
A Search for New Galactic Magnetars in Archival Chandra and XMM-Newton Observations
We present constraints on the number of Galactic magnetars, which we have
established by searching for sources with periodic variability in 506 archival
Chandra observations and 441 archival XMM-Newton observations of the Galactic
plane (|b|<5 degree). Our search revealed four sources with periodic
variability on time scales of 200-5000 s, all of which are probably accreting
white dwarfs. We identify 7 of 12 known Galactic magnetars, but find no new
examples with periods between 5 and 20 s. We convert this non-detection into
limits on the total number of Galactic magnetars by computing the fraction of
the young Galactic stellar population that was included in our survey. We find
that easily-detectable magnetars, modeled after persistent anomalous X-ray
pulsars, could have been identified in 5% of the Galactic spiral arms by mass.
If we assume there are 3 previously-known examples within our random survey,
then there are 59 (+92,-32) in the Galaxy. Transient magnetars in quiescence
could have been identified throughout 0.4% of the spiral arms, and the lack of
new examples implies that <540 exist in the Galaxy (90% confidence). Similar
constraints are found by considering the detectability of transient magnetars
in outburst by current and past X-ray missions. For assumed lifetimes of 1e4
yr, we find that the birth rate of magnetars could range between 0.003 and 0.06
per year. Therefore, the birth rate of magnetars is at least 10% of that for
normal radio pulsars. The magnetar birth rate could exceed that of radio
pulsars, unless the lifetimes of transient magnetars are >1e5 yr. Obtaining
better constraints will require wide-field X-ray or radio searches for
transient X-ray pulsars similar to XTE J1810--197, AX J1845.0--0250, CXOU
J164710.2--455216, and 1E 1547.0-5408.Comment: 16 pages, 10 figures, one with a bit of color. submitted to Ap
Random matrix techniques in quantum information theory
The purpose of this review article is to present some of the latest
developments using random techniques, and in particular, random matrix
techniques in quantum information theory. Our review is a blend of a rather
exhaustive review, combined with more detailed examples -- coming from research
projects in which the authors were involved. We focus on two main topics,
random quantum states and random quantum channels. We present results related
to entropic quantities, entanglement of typical states, entanglement
thresholds, the output set of quantum channels, and violations of the minimum
output entropy of random channels
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
Random graph states, maximal flow and Fuss-Catalan distributions
For any graph consisting of vertices and edges we construct an
ensemble of random pure quantum states which describe a system composed of
subsystems. Each edge of the graph represents a bi-partite, maximally entangled
state. Each vertex represents a random unitary matrix generated according to
the Haar measure, which describes the coupling between subsystems. Dividing all
subsystems into two parts, one may study entanglement with respect to this
partition. A general technique to derive an expression for the average
entanglement entropy of random pure states associated to a given graph is
presented. Our technique relies on Weingarten calculus and flow problems. We
analyze statistical properties of spectra of such random density matrices and
show for which cases they are described by the free Poissonian
(Marchenko-Pastur) distribution. We derive a discrete family of generalized,
Fuss-Catalan distributions and explicitly construct graphs which lead to
ensembles of random states characterized by these novel distributions of
eigenvalues.Comment: 37 pages, 24 figure
Toolbox for Discovering Dynamic System Relations via TAG Guided Genetic Programming
Data-driven modeling of nonlinear dynamical systems often require an expert
user to take critical decisions a priori to the identification procedure.
Recently an automated strategy for data driven modeling of \textit{single-input
single-output} (SISO) nonlinear dynamical systems based on \textit{Genetic
Programming} (GP) and \textit{Tree Adjoining Grammars} (TAG) has been
introduced. The current paper extends these latest findings by proposing a
\textit{multi-input multi-output} (MIMO) TAG modeling framework for polynomial
NARMAX models. Moreover we introduce a TAG identification toolbox in Matlab
that provides implementation of the proposed methodology to solve multi-input
multi-output identification problems under NARMAX noise assumption. The
capabilities of the toolbox and the modelling methodology are demonstrated in
the identification of two SISO and one MIMO nonlinear dynamical benchmark
models
Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product
Given two positive integers and and a parameter , we
choose at random a vector subspace of dimension . We show that the
set of -tuples of singular values of all unit vectors in fills
asymptotically (as tends to infinity) a deterministic convex set
that we describe using a new norm in .
Our proof relies on free probability, random matrix theory, complex analysis
and matrix analysis techniques. The main result result comes together with a
law of large numbers for the singular value decomposition of the eigenvectors
corresponding to large eigenvalues of a random truncation of a matrix with high
eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio
Convex optimization of programmable quantum computers
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any finite-dimensional design of this model is known to be non-universal, meaning that the processor cannot perfectly simulate an arbitrary quantum channel over the input. Characterizing how close the simulation is and finding the optimal program state have been open questions for the past 20 years. Here, we answer these questions by showing that the search for the optimal program state is a convex optimization problem that can be solved via semi-definite programming and gradient-based methods commonly employed for machine learning. We apply this general result to different types of processors, from a shallow design based on quantum teleportation, to deeper schemes relying on port-based teleportation and parametric quantum circuits
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