Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography

TL;DR

This thesis explores randomized dynamical decoupling methods to improve quantum memory stability and introduces enhanced one-way quantum key distribution protocols with noisy preprocessing to increase secure key rates.

Contribution

It develops novel randomized decoupling strategies and demonstrates their potential for protecting quantum computations, along with improved key rate protocols for quantum cryptography.

Findings

Randomized decoupling strategies outperform deterministic ones in preserving quantum memory.

Noisy preprocessing combined with structured codes increases secure key rates.

Iterative preprocessing further enhances quantum key distribution efficiency.

Abstract

The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual imperfections in a quantum memory. The suppression is achieved by altering the dynamics of an imperfect quantum memory with the help of a sequence of local unitary operations applied to the qudits. Whereas up to now the operations of such decoupling sequences have been constructed in a deterministic fashion, strategies are developed in this thesis which construct the operations by random selection from a suitable set. Furthermore, it is investigated if and how the discussed decoupling strategies can be employed to protect a quantum computation running on the quantum memory. The second part of the thesis deals with quantum error-correcting codes and protocols for quantum key distribution. The focus is on the BB84 and the 6-state protocol making use of only one-way communication during the error correction and privacy amplification steps. It is shown that by adding additional errors to the preliminary key (a process called noisy preprocessing) followed by the use of a structured block code, higher secure key rates may be obtained. For the BB84 protocol it is shown that iterating the combined preprocessing leads to an even higher gain.