Construction of Random Unitary Operations for Asymptotic Preparation of Werner States

Abstract

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.