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arXiv:quant-ph/0612216

In praise of measurement

N. David Mermin

Published Dec 27, 2006• 1 citation
arXivHTMLPDF

Abstract

The role of measurement in quantum computation is examined in the light of John Bell's critique of the how the term ``measurement'' is used in quantum mechanics. I argue that within the field of quantum computer science the concept of measurement is precisely defined, unproblematic, amd forms the foundation of the entire subject.

DOI
10.48550/arxiv.quant-ph/0612216

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The role of measurement in quantum computation is examined in the light of John Bell's critique of the how the term ``measurement'' is used in quantum mechanics. I argue that within the field of quantum computer science the concept of measurement is precisely defined, unproblematic, amd forms the foundation of the entire subject.
Introduction John S. Bell, of course, is best known for the result now referred to simply as “Bell's theorem,” which removed from consideration the class of so-called local hidden-variable theories that at the time of its publishing appeared to be the most natural class of theories among those that would render quantum mechanics a form of statistical mechanics. If, as this and other results suggest, quantum theory is to serve as a truly fundamental theory, conceptual precision in its interpretation is not only desirable but paramount. John Bell was accordingly concerned about what he viewed as conceptual imprecision, from the physical point of view, within the standard approaches to the theory. He saw this as most acute in the case of their treatment of measurement at the level of principle . His concerns were strongly expressed in the article “Against measurement” [1]. This was published in 1990 in a volume of proceedings of the 1989 Erice meeting “Sixty-Two Years of Uncertainty,” during which it was my pleasure to meet and eat with Bell, and to listen to him present this paper. He pointed out that this conceptual imprecision is reflected in the terminology of the foundations of quantum theory, a great deal of which he explicitly deemed worthy of banishment from discussions of principle, because it corresponds to a set of what he saw as vague and, in some instances, outright destructive concepts. His concern was thus not one regarding mathematics so much as regarding basic concepts used in contemporary quantum physics, which he viewed as failing the needs of natural philosophy and so of fundamental physics, despite their practical adequacy. Here, I consider John Bell's critique of standard quantum measurement theory and some alternative treatments wherein he saw greater conceptual precision, and make further suggestions as to how to improve conceptual precision, as he advocated. That the source of difficulties is to be understood specifically as a problem of imprecision of physical concepts that stands in the way of the achievement of an exact fundamental mechanical theory is pointed out at the outset of “Against measurement”: Bell wished to make it clear “at once that it is not mathematical precision, but physical” that caused him such great concern.
This book is an up-to-date introduction to the quantum theory of measurement, a fast developing field of intense current interest to scientists and engineers for its potential high technology applications. It is also a subject of importance to students for its central role in the foundations of quantum mechanics. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neumann and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as squeezed light, single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book contains a pedagogical introduction to the relevant theory written at a level accessible to those with only a modest background in quantum mechanics. It then goes on to discuss aspects of the design of practical quantum measurement systems. This book is essential reading for all scientists and engineers interested in the potential applications of technology near the quantum limit. It will also serve as an ideal supplement to standard quantum mechanics textbooks at the advanced undergraduate or graduate level.
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing physics is regarded as a creative activity to develop a meaningful description of the world, then one has to carefully discriminate between the two notions: An observer's account of experience - consitutive to meaning - is hardly expressed exhaustively by the formal framework of an interaction within one particular theory. We develop a corresponding perspective onto central terms in quantum mechanics in general, and onto the measurement problem in particular.