arXiv subjects
Publications and source records attributed to David Jakob Stonner.
We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular momentum formulation. Our analysis is based on novel weak-strong stability estimates which we combine with suitable reconstructions of the numerical solution. We present time-adaptive numerical simulations based on the a posteriori error estimators for solutions involving blow-up.
Twirling operations, which average a quantum state with respect to a unitary subgroup, have become a frequently-employed tool in quantum information processing. We investigate the efficient implementation of twirling operations with minimal resources, without necessitating the ability to perform all possible unitary operations on the quantum system of interest. We present a general algebraic method allowing us to choose a set of - typically very few - unitary operators which, when applied randomly and repeatedly, produce the given twirling operation exponentially quickly. The method is applied to twirling operations for bipartite quantum systems with respect to the unitary group $U(d)\otimes U(d)$, an essential ingredient in entanglement distillation protocols. In particular, we provide a complete classification of sets of unitary operators capable of performing twirling on two qubits. Moreover, we construct a generic set containing at most three unitary operators achieving the twirling operation for a general two-qudit system.
Werner states are defined as bipartite qudit states that remain unchanged under application of arbitrary unitary operators acting on both subsystems simultaneously. Their preparation is a crucial ingredient in entanglement distillation protocols. This thesis deals with an iterative approach to prepare Werner states asymptotically, using random unitary operations. The asymptotic dynamics of random unitary operations are linked to algebraic properties of the involved unitary operators applying results about general quantum operations. Then a family of random unitary operations is constructed, which prepares Werner states asymptotically for an arbitrary finite dimensional bipartite qudit system. Finally, this construction is applied in qubit and qudrit systems, where the convergence rate is optimized numerically.