Duvenhage, Rocco2024-01-242024-01-242024-042023-10-26*A2024http://hdl.handle.net/2263/94087Dissertation (MSc (Physics))--University of Pretoria, 2023.We analyse a formulation of the quantum Wasserstein distance of order $1$ and set up a general theory leading to a Wasserstein distance of order $1$ between the unital maps from one specific algebra to another specified algebra. This gives us a metric on the set of unital maps from one composite system to another, which is deeply connected to the reductions of the unital maps. We use the fact that channels are unital maps with extra structure, to systematically define a quantum Wasserstein distance of order $1$ between channels, i.e., a metric on the set of channels. Lastly, the additivity and stability properties of this metric are studied.en© 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDQuantum optimal transportQuantum Wasserstein distance of order 1Quantum channelsQuantum statesComposite systemsSustainable Development Goals (SDGs)SDG-04: Quality educationNatural and agricultural sciences theses SDG-04SDG-09: Industry, innovation and infrastructureNatural and agricultural sciences theses SDG-09Dissertationu18026312Disclaimer letter