788 research outputs found
The Jamio{\l}kowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number and -positive maps
Positive maps which are not completely positive are used in quantum
information theory as witnesses for convex sets of states, in particular as
entanglement witnesses and more generally as witnesses for states having
Schmidt number not greater than k. It is known that such witnesses are related
to k-positive maps. In this article we propose a new proof for the
correspondence between vectors having Schmidt number k and k-positive maps
using Jamiolkowski's criterion for positivity of linear maps; to this aim, we
also investigate the precise notion of the term "Jamiolkowski isomorphism". As
consequences of our proof we get the Jamiolkowski criterion for complete
positivity, and we find a special case of a result by Choi, namely that
k-positivity implies complete positivity, if k is the dimension of the smaller
one of the Hilbert spaces on which the operators act.Comment: 9 page
Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication
We investigate the error tolerance of quantum cryptographic protocols using
-level systems. In particular, we focus on prepare-and-measure schemes that
use two mutually unbiased bases and a key-distillation procedure with two-way
classical communication. For arbitrary quantum channels, we obtain a sufficient
condition for secret-key distillation which, in the case of isotropic quantum
channels, yields an analytic expression for the maximally tolerable error rate
of the cryptographic protocols under consideration. The difference between the
tolerable error rate and its theoretical upper bound tends slowly to zero for
sufficiently large dimensions of the information carriers.Comment: 10 pages, 1 figur
OPTIMIZATION OF SPEED PARAMETERS IN BURNISHING OF SAMPLES FABRICATED BY FUSED DEPOSITION MODELING
Fused Deposition Modeling (FDM) is one of the best Rapid Prototyping Processes proved to be. Many researchers have produced a lot of work using the FDM process and many papers were published. Many researchers have concentrated on optimizing the parameters to obtain higher surface finish. Burnishing is one of the processes used to get higher surface finish on light metals. The present paper deals with the application of burnishing process on the samples fabricated with FDM. The burnishing process is applied on the samples at different speeds and the surface finish results are recorded in the present experimentation
Symmetry breaking perturbations and strange attractors
The asymmetrically forced, damped Duffing oscillator is introduced as a
prototype model for analyzing the homoclinic tangle of symmetric dissipative
systems with \textit{symmetry breaking} disturbances. Even a slight fixed
asymmetry in the perturbation may cause a substantial change in the asymptotic
behavior of the system, e.g. transitions from two sided to one sided strange
attractors as the other parameters are varied. Moreover, slight asymmetries may
cause substantial asymmetries in the relative size of the basins of attraction
of the unforced nearly symmetric attracting regions. These changes seems to be
associated with homoclinic bifurcations. Numerical evidence indicates that
\textit{strange attractors} appear near curves corresponding to specific
secondary homoclinic bifurcations. These curves are found using analytical
perturbational tools
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution
figures is available at http://www.pks.mpg.de/~edugal
Disorder, spin-orbit, and interaction effects in dilute
We derive an effective Hamiltonian for in
the dilute limit, where can be described in
terms of spin polarons hopping between the {\rm Mn} sites and coupled
to the local {\rm Mn} spins. We determine the parameters of our model from
microscopic calculations using both a variational method and an exact
diagonalization within the so-called spherical approximation. Our approach
treats the extremely large Coulomb interaction in a non-perturbative way, and
captures the effects of strong spin-orbit coupling and Mn positional disorder.
We study the effective Hamiltonian in a mean field and variational calculation,
including the effects of interactions between the holes at both zero and finite
temperature. We study the resulting magnetic properties, such as the
magnetization and spin disorder manifest in the generically non-collinear
magnetic state. We find a well formed impurity band fairly well separated from
the valence band up to for which finite size
scaling studies of the participation ratios indicate a localization transition,
even in the presence of strong on-site interactions, where is the fraction of magnetically active Mn. We study the
localization transition as a function of hole concentration, Mn positional
disorder, and interaction strength between the holes.Comment: 15 pages, 12 figure
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