Quantum Key Distribution in the Non-Asymptotic Regime

TL;DR

This thesis reviews quantum key distribution protocols, especially BB84, focusing on their security in the non-asymptotic regime and analyzing quantum capacity for specific channels.

Contribution

It provides an overview of non-asymptotic security proofs for quantum key distribution and analyzes quantum capacity for amplitude damping channels.

Findings

Security proof for BB84 in non-asymptotic regime

Calculation of quantum capacity for amplitude damping channel

Overview of current state of prepare and measure protocols

Abstract

This is a Bachelor's thesis on quantum key distribution in the non-asymptotic regime submitted to the Leibniz Universit\"at Hannover, Germany. It deals with the question how to generate a key to encrypt messages between two honest parties that an eavesdropper does not gain any information about. The purpose of this thesis is to give an overview over the current state of the prepare and measure quantum key distribution protocol and its security proof with a specific focus on the non-asymptotic case. Therefore, we present the different steps of the protocol and retrace them with the help of the BB84-protocol. Afterwards, the security proof of this protocol is introduced and in the end, we have a closer look at the quantum capacity and calculate it for the amplitude damping channel.