Construction of Random Unitary Operations for Asymptotic Preparation of Werner States

TL;DR

This paper presents an iterative method using random unitary operations to asymptotically prepare Werner states in bipartite qudit systems, with optimized convergence rates demonstrated numerically.

Contribution

It introduces a novel construction of random unitary operations that asymptotically generate Werner states for any finite-dimensional bipartite system.

Findings

Constructed a family of random unitaries for Werner state preparation

Linked asymptotic dynamics to algebraic properties of unitaries

Optimized convergence rates numerically in qubit and qudit systems

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.