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New scientific paradigms typically consist of an expansion of the conceptual language with which we describe the world. Over the past decade, theoretical physics and quantum information theory have turned to category theory to model and reason about quantum protocols. This new use of categorical and algebraic tools allows a more conceptual and insightful expression of elementary events such as measurements, teleportation and entanglement operations, that were obscured in previous formalisms. Recent work in natural language semantics has begun to use these categorical methods to relate grammatical analysis and semantic representations in a unified framework for analysing language meaning, and learning meaning from a corpus. A growing body of literature on the use of categorical methods in quantum information theory and computational linguistics shows both the need and opportunity for new research on the relation between these categorical methods and the abstract notion of information flow. This book supplies an overview of how categorical methods are used to model information flow in both physics and linguistics. It serves as an introduction to this interdisciplinary research, and provides a basis for future research and collaboration between the different communities interested in applying category theoretic methods to their domain's open problems.
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~= ~ QUANTUM PHYSICS AND LINGUISTICS A Compositional, Diagrammatic Discourse Editedby CHRIS HEUNEN MEHRNOOSH SADRZADEH EDWARD GREFENSTETTE Quantum Physics and Linguistics This page intentionally left blank QUANTUM PHYSICS AND LINGUISTICS A Compositional, Diagrammatic Discourse Edited by CHRIS HEUNEN MEHRNOOSH SADRZADEH and EDWARD GREFENSTETTE University of Oxford, Department of Computer Science OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. lt furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Oxford University Press 2013 Chapter 3 © Ross Duncan The moral rights of the authors have been asserted First Edition published in 2013 Impression: 1 Ali rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographies rights organization. Enquiries concerning reproduction outside the scope of the ab ove should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 978-0-19-964629-6 Printed and bound by CP! Group (UK) Ltd, Croydon, CRO 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. PREFACE Q uantum mechanics and linguistics appear to be quite unrelated at first sight. Yet significant parts ofboth concern compositional reasoning about the way information flows among subsystems and the manner in which this flow gives ri se to the properties of a system as a wh ole. This book is about the mathematics underlying this notion of compositionality, how it gives ri se to intuitive diagrammatic calculi, and how these compositional methods are applied to reas