The Jamio{\l}kowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number kk and kk-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 $d$-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 Ga1−xMnxAs{\rm Ga}_{1-x}{\rm Mn}_x{\rm As}

We derive an effective Hamiltonian for ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ in the dilute limit, where ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ can be described in terms of spin $F=3/2$ 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 $x_{\rm active} \lesssim 0.015$ for which finite size scaling studies of the participation ratios indicate a localization transition, even in the presence of strong on-site interactions, where $x_{\rm active}<x_{\rm nom}$ 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