A philosophical treatise of high caliber, Christopher G. Timpson’s book draws on insights from the philosophy of language, from general philosophy of science, from epistemology, and from metaphysics to inform detailed analyses of the concept of quantum information, of its role in quantum informational protocols, and of its significance for the wider philosophy of quantum mechanics. Those with a philosophical interest in the concept of information (quantum or otherwise) and in information-theoretic approaches to science are strongly encouraged to read this work. Those interested in the philosophy of quantum information theory in particular, and in its significance for the foundations of quantum mechanics, would be unwise not to.

The book is very well and clearly written: the prose is lucid and the structure is transparent, and despite the intricacy and complexity of the subject matter, it is accessible to a wide audience. For the most part it is also self-contained, in the sense that one need not draw on outside sources in order to comprehend, at least superficially, the content and subject matter of the book. Thus, in addition to being a scholarly work of high importance, it is suitable to read as part of a graduate (or advanced undergraduate) philosophy seminar dealing with these topics. Indeed any graduate course on the philosophy of quantum information whose syllabus did not include at least a portion of this book would, in my opinion, be lacking.

Regarding the content, let me begin with a few words about what the book is not. First, those hoping to learn the science of quantum information should look elsewhere. Timpson’s exposition of the technical machinery of classical (i.e., Shannon) and quantum information theory is done in a clear, careful, and accessible manner, and for its primarily philosophical purposes the book is for the most part self-contained. However, Timpson’s book is no substitute for a more thoroughgoing technical introduction to the topic such as Nielsen and Chuang’s classic text. The book is also nowhere near to a comprehensive survey of all of the philosophically interesting research currently being done in quantum information theory. There is little or no mention, for instance, of information-theoretic measures of quantum correlations or of the resource theory of entanglement or of their potential (or lack thereof) for illuminating quantum foundations. Neither is the book devoted in any really significant way to quantum computation. Timpson’s three-page discussion of quantum computation in his expository chapter on quantum information theory is largely superficial. His otherwise quite illuminating chapter on the status of David Deutsch’s “Turing principle” is neither an introduction to quantum computation nor a detailed analysis of how quantum computers work, nor is it even (at least for me) a discussion of one of the more pressing philosophical issues related to the science of quantum computing in particular. Thus, those wishing to learn more about these topics are advised, again, to look elsewhere. But with respect to its actual goals—of clarifying the concept of quantum information and of clarifying the relation of the theory of quantum information to the foundations of quantum mechanics—the book is highly relevant, wonderfully executed, and its claims are powerfully argued for.

“Information,” for Timpson, is an abstract noun, and one can explicate it most generally in terms of the verb “inform.” In the “everyday” sense, to inform is to make known to someone something that was previously unknown; it thus involves and is closely associated with such concepts as knowledge, language, meaning, and person. Not so for the technical sense of inform, which is the object of both the Shannon and quantum theories of information. The failure to recognize that there is a distinction between these two senses has, according to Timpson, led to a number of confusions in the philosophical literature on information (such as Dretske’s “semantic naturalism,” discussed in chap. 2). As for the main topic of concern of the book,it is information in its technical sense: what Timpson refers to as “information_t.”

Timpson defines information_t as “what is provided by an information_t source that is required to be reproducible at the destination if the transmission is to be counted a success” (22). Just what this something provided by an information_t source—what a piece of information_t—is, for Timpson, is most correctly thought of as a type. For instance, a sequence such as x ₂x ₄x ₁x ₉ … x ₆x ₈x ₃x ₁x ₂ (in the quantum case the x_i will be quantum state descriptions) is a type that is capable of being instantiated by various concrete tokens (one of which is the particular collection of markings printed on this page). It is not these tokens that are required to be transmitted if the communication is to count as being successful. Rather, what is required is only that another token of this type be produced at the destination. Thus, it is the type that must be transmitted. Once we are clear on this (i.e., on the fact that information_t transfer does not essentially consist in the flow of some spatiotemporally located thing called “the information_t”), then we see, according to Timpson, how to dissolve many of the mysteries associated with quantum informational protocols like quantum teleportation (chap. 4). And just in case one thought the approach of Deutsch and Hayden might be used to explicate a notion of quantum information “flow,” Timpson’s fifth chapter should convince one that this approach is not viable for that purpose.

So much for what (quantum) information is. In the last part of the book, Timpson takes up the relation between quantum information theory and the foundations of quantum mechanics and, along the way, evaluates a few of the more important extant information-theoretic approaches to quantum foundations. These include, most notably, the information-theoretic axiomatization of quantum mechanics due to Clifton, Bub, and Halvorson (CBH), as well as the quantum Bayesianism of Caves, Fuchs, and Schack. Timpson’s discussion of the latter in particular is remarkable for its clarity and magnanimity. The proponent of quantum Bayesianism is no “straw man” under Timpson’s treatment, and Timpson dismembers many of the more common objections to the view (chap. 9), before presenting a number of other more serious (although not insurmountable) challenges (chap. 10). In the end, however, the question of the viability of quantum Bayesianism is, for Timpson, largely orthogonal to the question of the relevance of information theory to the foundations of quantum mechanics. For the quantum Bayesian, the quantum state description is nothing more than a representation of our subjective degree of belief regarding the probabilities of various experimental outcomes. Information, however, is factive, and hence inherently objective. Thus, whatever we think of the merits of the view, the quantum state description cannot represent information for the quantum Bayesian (203). Timpson’s evaluation (chap. 8) of CBH’s axiomatic approach to the link between information theory and quantum mechanics is also negative. It is not the case, Timpson argues, that the CBH characterization theorem shows us that the aim of fundamental physics is to represent and manipulate information, nor is it the case that the CBH characterization theorem shows that quantum mechanics must be interpreted as a principle theory like Special Relativity.

Without doubt, Timpson’s deflationary explication of information_t represents an important positive contribution to the philosophy of (quantum) information. Nevertheless, the overall thrust of Timpson’s monograph (in the second half especially) is negative. Thus, regarding the relation between quantum information theory and fundamental physics, quantum information theory does not, for Timpson, add a new kind of stuff to our catalog of physical concepts, nor, for Timpson, does it demand that we reinterpret our existing physical concepts in light of it. But what can we say that is positive about the relation between quantum information theory and quantum mechanics? Timpson does make a few gestures in this direction: quantum information theory contributes to our understanding of the foundations of quantum mechanics by encouraging us to ask new kinds of questions and by suggesting new frameworks for inquiry; moreover, it highlights the fact that progress in theoretical physics need not always be made by successfully postulating new kinds of stuff (239). This is all very well said. However, apart from an all-too-short discussion of generalized probability theories in chapter 8, section 4 Timpson does very little more than make gestures at these potential positive contributions. Yet it is precisely these that I, and I am sure many others, would have preferred to read about. In fairness to Timpson, however, it is sometimes necessary to clear the road of obstacles before one ventures to travel down it.

In any case, let me reiterate that Timpson’s book is a must read for those interested in the topic of quantum information theory. Moreover, it is an important contribution to the philosophy of information theory in general, and I have no doubt that it will be much discussed in the years to come.