Uncertainty relations for general phase spaces

We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow an arbitrary choice of metric for the distance of outcomes, and the choice of an exponent distinguishing e.g., absolute or root mean square deviations. The emphasis of the article is on developing a unified treatment, in which one observable takes values in an arbitrary locally compact abelian group and the other in the dual group. In all cases the phase space symmetry implies the equality of measurement uncertainty bounds and preparation uncertainty bounds, and there is a straightforward method for determining the optimal bounds.Comment: For the proceedings of QCMC 201

Dynamically generated edge states in topological Kondo insulators

Kondo insulators combine strong electronic correlations with spin orbit coupling and thereby provide a potential realization of correlated topological insulators. We present model calculations which allow us to study the onset of bulk coherence and concomitant topological edge states from the mixed valence to local moment regimes. Our real-space dynamical mean-field results include the detailed temperature dependence of the single particle spectral function on slab geometries as well as the temperature dependence of the topological invariant. The relevance of our calculations for candidate materials like SmB6 is discussed.Comment: 7 pages, 6 figure

Iterative Optimization of Quantum Error Correcting Codes

We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds codes outside the usual Knill-Laflamme definition of error correcting codes. The iteration is shown to improve the figure of merit "channel fidelity" in every step.Comment: 5 pages, 2 figures, REVTeX 4; stability of algorithm include

Optimal Cloning of Pure States, Judging Single Clones

We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state \sigma into M>N systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma. In a previous paper it was shown that this problem has a unique optimal solution, when the quality of the output is judged by arbitrary measurements, involving also the correlations between the clones. We show in this paper, that if the quality judgement is based solely on measurements of single output clones, there is again a unique optimal cloning device, which coincides with the one found previously.Comment: 16 Pages, REVTe