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Cambridge University Press eBooks

Epilogue: What Does It All Mean?

Andrew N. Jordan, Irfan A. Siddiqi

Published Feb 15, 2024• 0 citations
Publisher

Abstract

The book concludes in Chapter 11, where we give in our epilogue a more philosophical reflection on the state of the field. We discuss what it all means, where the field is going, how quantum computers are the ultimate test of quantum mechanics, and speculate on a future post-quantum science.
DOI
10.1017/9781009103909.012

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Abstract The strange behaviour of photons described at the end of the last chapter immediately raises all sorts of questions about the meaning of quantum theory. We might be encouraged to look for this meaning by going back to the theory’s mathematical structure: perhaps by trying to find out how we might better interpret some of its elements. However, it is a central argument of this book that, no matter where we look, we are always led back to philosophy. At first sight, this might seem to be an odd thing to claim. After all, modern textbooks on quantum physics and chemistry rarely (if ever) discuss philosophy. We accept that the behaviour of photons is strange, but surely it is something that we can at least study experimentally-do we need philosophy in these circumstances? But this is the whole point. Quantum theory directly challenges our understanding of the nature of the fundamental particles and the process of measurement, and we cannot go forward unless we adopt some kind of interpretation. As we will see, this interpretation has to be based on some philosophical position.
After going through the chapter on entanglement you will have reached the end of our book. As the subtitle suggests, its aim was literally to present an introduction to the subject of quantum entanglement. We have left untouched several important aspects of quantum entanglement, including multipartite systems, infinite-dimensional systems and continuous variables. Moreover, we believe that some key ideas presented in the book might be extended much further then we have managed to do. For instance the maps–states duality, illustrated in Chapter 11, might be used to find relations between capacities of quantum channels and measures of entanglement of the corresponding states of an extended system. In the book we have consistently used a geometric approach to highlight similarities and differences between the classical and quantum spaces of states. What is the knowledge gained by studying the book good for? We hope it will contribute to a better understanding of quantum mechanics. We hope also that it will provide a solid foundation for a new, emerging field of science – the theory of quantum information processing. Quantum entanglement plays a decisive role in all branches of the field including quantum cryptography, quantum error correction and quantum computing. In trying to describe the intricate geometry of the space of quantum states, we have deliberately restricted ourselves to discussing the statics of quantum theory. We have presented the arena, in which quantum information can be processed. We have not attempted to inject any concrete dynamics into our arena, but hope that readers equipped with some knowledge of its properties may introduce into it spectacular action.
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