Decomposability of Linear Maps under Tensor Products

Both completely positive and completely copositive maps stay decomposable under tensor powers, i.e under tensoring the linear map with itself. But are there other examples of maps with this property? We show that this is not the case: Any decomposable map, that is neither completely positive nor completely copositive, will lose decomposability eventually after taking enough tensor powers. Moreover, we establish explicit bounds to quantify when this happens. To prove these results we use a symmetrization technique from the theory of entanglement distillation, and analyze when certain symmetric maps become non-decomposable after taking tensor powers. Finally, we apply our results to construct new examples of non-decomposable positive maps, and establish a connection to the PPT squared conjecture.Comment: 26 pages, 3 figure

All unital qubit channels are 44-noisy operations

We show that any unital qubit channel can be implemented by letting the input system interact unitarily with a $4$-dimensional environment in the maximally mixed state and then tracing out the environment. We also provide an example where the dimension of such an environment has to be at least $3$.Comment: 8 pages, no picture

Femtosecond electrons probing currents and atomic structure in nanomaterials

The investigation of ultrafast electronic and structural dynamics in low-dimensional systems like nanowires and two-dimensional materials requires femtosecond probes providing high spatial resolution and strong interaction with small volume samples. Low-energy electrons exhibit large scattering cross sections and high sensitivity to electric fields, but their pronounced dispersion during propagation in vacuum so far prevented their use as femtosecond probe pulses in time-resolved experiments. Employing a laser-triggered point-like source of either divergent or collimated electron wave packets, we developed a hybrid approach for femtosecond point projection microscopy and femtosecond low-energy electron diffraction. We investigate ultrafast electric currents in nanowires with sub-100 femtosecond temporal and few 10 nm spatial resolutions and demonstrate the potential of our approach for studying structural dynamics in crystalline single-layer materials.Comment: 18 pages, 4 figures, includes 8 pages supplementary informatio

Local chain ordering in amorphous polymer melts: Influence of chain stiffness

Molecular dynamics simulation of a generic polymer model is applied to study melts of polymers with different types of intrinsic stiffness. Important static observables of the single chain such as gyration radius or persistence length are determined. Additionally we investigate the overall static melt structure including pair correlation function, structure function and orientational correlation function.Comment: 13 pages, 15 figures, PCCP accepte