Unital Quantum Channels – Convex Structure and Revivals of Birkhoff’s Theorem

The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to O(d)-covariant channels this leads to a complete characterization and reveals a remarkable feature: instances of channels which are not in the convex hull of unitaries can become elements of this set by either taking two copies of them or supplementing with a completely depolarizing channel. These scenarios imply that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.     

Über die Mittelwerte und Koeffizienten multivalenter Funktionen

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Competence-driven project portfolio selection,scheduling and staff assignment

This paper presents a new model for project portfolio selection, paying specific attention to competence development. The model seeks to maximize a weighted average of economic gains from projects and strategic gains from the increment of desirable competencies. As a sub-problem, scheduling and staff assignment for a candidate set of selected projects must also be optimized. We provide a nonlinear mixed-integer program formulation for the overall problem, and then propose heuristic solution techniques composed of (1) a greedy heuristic for the scheduling and staff assignment part, and (2) two (alternative) metaheuristics for the project selection part. The paper outlines experimental results on a real-world application provided by the E-Commerce Competence Center Austria and, for a slightly simplified instance, presents comparisons with the exact solution computed by CPLEX.     

Convergence of the Magnus Series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.