Metascience DOI 10.1007/s11016-014-9890-y BOOK REVIEW
Thinking carefully about quantum information Christopher G. Timpson: Quantum information theory and the foundations of quantum mechanics. Oxford: Oxford University Press, 2013, 293pp, $85.00 HB Armond Duwell
Ó Springer Science+Business Media Dordrecht 2014
The development of quantum information theory over the last 20 years has produced a plethora of interesting new results and along with them a host of claims have been made by physicists and philosophers about how quantum information theory helps us understand the quantum world. When one examines such claims with any attention to detail, it is quite obvious that radically different and incompatible claims are being made about the quantum world. Christopher Timpson’s Quantum Information Theory and the Foundations of Quantum Mechanics provide a sober and thorough critical guide to these claims. Claims made about how quantum information theory can help us understand the quantum world are a motley collection, and so too are the chapters of Timpson’s book. That said, they can almost be sorted into two broad categories: those that aim to define quantum information and to understand the quantum world in terms of it, and those that aim to reconstruct quantum mechanics in terms of informationtheoretic axioms which will render the quantum world understandable to us. Timpson’s Chapter 6, on quantum computation is the exception. Oftentimes, different concepts of information are deployed in the literature associated with quantum information theory that are as much related as Michael Jackson the pop music icon and Michael Jackson the beer and whisky expert. It is strikingly ironic how much confusion has been generated by appeal to concepts of information. Timpson’s second chapter, ‘‘What is information?’’, is the antidote to such confusion. Timpson claims that there are really only two proper ways to talk about information in this context: the everyday way, which has a strong connection to knowledge, and the technical way, whose roots lie in Shannon (1948). With respect to both, Timpson’s most pressing point is to guard against a view that
A. Duwell (&) Department of Philosophy, University of Montana, 32 Campus Dr #5780, Missoula, MT 59812-5780, USA e-mail:
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information is a concrete entity or substance, a mistaken view that has appeared too often in the literature. The most important contribution of this chapter is a definition of the technical concept of information which is a generalization of Shannon’s concept of information. Timpson defines the technical notion of information, denoted by Informationt as (22): Informationt is what is produced by an Informationt source that is required to be reproducible at the destination if the transmission is to be counted as a success. One specializes the definition to the classical (Shannon) concept of information simply by adding ‘‘classical’’ before ‘‘Informationt’’ in the definition, and similar with the quantum concept of information. It is quite interesting that this generalized definition of information might be apt to specialize to genetic information, or biological information, or any host of other kinds of information one might define. It follows from the definition of Informationt that it is not a concrete entity or substance. Why? Because, as Timpson tells us, what is required to be reproducible at a destination in order for the transmission to be a success is not the actual thing (the token) that was produced by the source, but rather the pattern produced by the source (the type) that needs to be reproducible at the destination. Types are abstract entities, not concrete ones, thereby establishing this important point. The work done in Chapter 2 sets the stage for a careful analysis of quantum information in Chapter 3. In Chapter 3, Timpson advocates a concept of quantum information that is commensurate with Schumacher’s (1995) work on the concept of quantum information, which itself has close affinities to Shannon’s (1948) analysis of information. Timpson shows that quantum information can be defined as a specialization of Informationt. With the classical and quantum concepts firmly in grasp, their similarities and differences are carefully laid out, and a number of confusions are laid to rest, especially regarding how information can be said to be physical. Early literature in quantum information theory focused on the peculiarities of quantum information transfer, in particular the use of entanglement to do so. Chapter 4 shows how many puzzles about quantum information transfer can be dissolved in virtue of recognizing that information, in the everyday or technical senses, is not a concrete entity or substance. The point is made abundantly clear by a close study of quantum teleportation, a paradigm example of quantum information transfer which is markedly different than any information transfer using classical systems. Timpson emphasizes, quite rightly, that if one wants to know how information is transferred in quantum systems, one must appeal to the properties of these systems that allows one to reproduce what was produced by the quantum source. To do that, one must appeal to interpretations of quantum mechanics that specify what the properties of quantum systems are. Timpson shows us how very different stories about information transfer arise depending on what interpretation of quantum mechanics one adopts. Chapter 5 considers the work of Deutsch and Hayden (2000) who claim that contrary to appearances, information flows locally in entangled quantum subsystems. Timpson points out that information cannot properly be said to flow because
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information is not an entity or substance. That said, with suitable qualification, information flow can be understood to flow insofar as a system whose properties are correlated with an information source moves in a continuous spatio-temporal path from one end of a communication system to another. The work that Deutsch and Hayden need to do to make good on this claim is indicate how the properties of the system in question (a member of an entangled pair) are suited to the task. Toward this end, Deutsch and Hayden propose shifting to the Heisenberg representation of the state of the quantum systems involved in the information transfer scheme instead of the Schroedinger representation. When we make this shift, information does appear to be flowing from one end of the communication system to the other. Here, the lesson from the previous chapter finds application: No story about how information is transferred is complete in the quantum case unless an interpretation is specified. Timpson argues that Deutsch and Hayden’s analysis admits of two very different interpretations, and their claims do not hold on one. Timpson points out that while they do hold on the other interpretation, that interpretation has some serious drawbacks. In fact, Wallace and Timpson (2007) argue that this alternative interpretation in which Deutsch and Hayden’s (2000) claims hold is actually unacceptable. The second half of the book considers some attempts to find foundational principles that can be used to recover some of and preferably all of the structure of quantum mechanics. The goal is not simply to find principles that will get the job done, for any axiomatization of quantum mechanics would do, but to find principles whose meaning is easy to grasp. Chapter 8 examines two attempts: that of Zeilinger (1999), and that of Clifton et al. (2003). Timpson’s method of analysis here alters course. Instead of primarily utilizing results developed earlier in the book, he shifts to examining whether the particular principles proposed can be put to the use intended of them, and moreover, whether the foundational principles proposed are reasonable to adopt. While this work is superb, one of the most important points made in this chapter is that even if a set of the preferred kind of principles were to be discovered, philosophical work would not end at that stage. Whatever the principles discovered might be, they will pick the exact same structure physicists and philosophers have been contemplating for the last 85 or so years. That structure is something which requires an interpretation, and information-theoretic principles alone will not specify what the ontology of the world is. Chapters 9 and 10 consider the subjective quantum Bayesianism of Fuchs, Cave, and Schack (CFS) (Caves et al. 2002a, b, c, 2007; Fuchs 2003; Fuchs and Schack 2004, and others). Instead of proposing principles that would help us understand the quantum world, CFS propose an austere, but non-instrumentalist interpretation of quantum mechanics which is meant to aid in finding such principles. Their starting point is to interpret quantum probabilities as subjective degrees of belief. One quickly finds that the only coherent way to do this is to interpret quantum states and operations subjectively as well. The payoffs of such a view, if it were to work, come straightaway. Quantum mechanics is perfectly local since state change of a distant system based on local actions is interpreted as nothing more than an update of one’s subjective beliefs about the distant system. Moreover, the measurement problem dissolves since there are necessary and sufficient conditions for state change: a state
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change is warranted if and only if one’s beliefs about a system change, and they might change as the result of learning the outcome of a measurement process. Immediate potential payoffs aside, it is an understatement to say that CFS’s subjective quantum Bayesianism has generated a lot of heat. Timpson does a fine job of converting that to light. In these chapters, Timpson makes quick work of several objections against the view: that it is instrumentalist or solipsist, and that it cannot make sense of Wigner’s friend scenarios. He also does the view a great service by articulating an ontology for the view that makes clear that, subjective elements notwithstanding, it is very much a realist view of the quantum world. He is also critical of the view and raises several problems for it that have no easy solutions: reconciling the explanatory power of the theory with subjective quantum Bayesianism’s central tenants, and a type of Moore’s paradox for the view. For anyone interested in how quantum information theory can possibly help us understand the world, Timpson’s book is essential reading. For no matter what particular area of quantum information theory one is interested in, one will find a related discussion in Timpson’s book that demonstrates how to think clearly about information in that context, what the crucial issues are, and how to properly navigate them.
References Caves, C.M., C.A. Fuchs, and R. Schack. 2002a. Conditions for compatibility of state assignments. Physical Review A 66(6): 062111. Caves, C.M., C.A. Fuchs, and R. Schack. 2002b. The quantum de Finetti representation. Journal of Mathematical Physics 43(9): 4537. Caves, C.M., C.A. Fuchs, and R. Schack. 2002c. Quantum probabilities as Bayesian probabilities. Physical Review A 65: 022305. Caves, C.M., C.A. Fuchs, and R. Schack. 2007. Subjective probability and quantum certainty. Studies in History and Philosophy of Modern Physics 38: 255–274. Clifton, R., J. Bub, and H. Halvorson. 2003. Characterizing quantum theory in terms of information theoretic constraints. Foundations of Physics 33(11): 1561. Deutsch, D., and P. Hayden. 2000. Information flow in entangled quantum subsystems. Proceedings of the Royal Society of London A 456: 1759–1774. Fuchs, C.A. 2003. Quantum mechanics as quantum information, mostly. Journal of Modern Optics 50: 987. Fuchs, C.A., and R. Schack. 2004. Unknown quantum states and operations: A Bayesian view. In ˇ eha´cˇek, 147–187. Quantum state estimation, Lecture Notes in Physics, ed. M.G.A. Paris, and J. R Berlin: Springer. Schumacher, B. 1995. Quantum coding. Physical Review A 41(4): 2738. Shannon, C.E. 1948. The mathematical theory of communication. Bell Systems Technical Journal 27(279–423, 623–656). Wallace, D., and C.G. Timpson. 2007. Non-locality and gauge freedom in Deutch and Hayden’s formulation of quantum mechanics. Foundations of Physics 37(6): 951–955. Zeilinger, A. 1999. A foundational principle for quantum mechanics. Foundations of Physics 29(4): 631–643.
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