Rochus Klesse

Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wave functions at the transition energy are obtained within the framework of the generalized Chalker-Coddington network model. We determine the critical exponent α0 characterizing the scaling behaviour of the local order parameter for systems with potential correlation length d up to 12 magnetic lengths l. Our results show that α0 does not depend on the ratio d/l. With increasing d/l, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behaviour on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.

Distance dependence of entanglement generation via a bosonic heat bath.

Within a generalized Caldeira-Leggett model, we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance r. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a microscopic distance that is of order of the cutoff wavelength lambda of the system-bath interaction. At larger distances, the maximal entanglement is exponentially suppressed with a decay length of order lambda. We conclude that entanglement generation via a heat bath is not suitable for entangling remote objects.

A Random Coding Based Proof for the Quantum Coding Theorem

We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannons original treatment of information transmission via a noisy classical channel.

Experimental studies of Coulomb drag between ballistic quantum wires

The Coulomb drag between two spatially separated one-dimensional (1D) electron systems in lithographically fabricated 2??m long quantum wires is studied experimentally. The drag voltage VD shows peaks as a function of a gate voltage which shifts the position of the Fermi level relative to the 1D subbands. The maximum in VD and the drag resistance RD occurs when the 1D subbands of the wires are aligned and the Fermi wave vector is small. The drag resistance is found to decrease exponentially with interwire separation. In the temperature region 0.2?K?T?1?K, RD decreases with increasing temperature in a power-law fashion RDTx with x ranging from -0.6 to -0.77 depending on the gate voltage. We interpret our data in terms of the Tomonaga-Luttinger liquid theory.

Quantum Error Correction in Spatially Correlated Quantum Noise

We consider quantum error correction of quantum noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kinds of noise correlations have a strong negative impact on quantum error correction.

SPECTRAL COMPRESSIBILITY AT THE METAL-INSULATOR TRANSITION OF THE QUANTUM HALL EFFECT

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent

Approximate quantum error correction, random codes, and quantum channel capacity

\eta

Coulomb drag between ballistic one-dimensional electron systems

and the spectral compressibility

Coulomb drag between quantum wires

\chi

Spatial and spectral multifractality of the local density of states at the mobility edge

at the mobility edge,