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arXiv:quant-ph/0211089 · Foundations of Physics

Characterizing Quantum Theory in Terms of Information-Theoretic Constraints

Rob Clifton, Jeffrey Bub, Hans Halvorson

Published Oct 24, 2003• 369 citations
arXivHTMLPDF
DOI
10.1023/a:1026056716397

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This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003); quant-ph/0211089). I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003); quant-ph/0211089). I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
Does information play a significant role in the foundations of physics? We investigate whether information-theoretic constraints characterize quantum theory. In a C*-algebraic framework, this is known to hold via three equivalences: no broadcasting and noncommutativity; no bit commitment and nonlocality; no signalling and kinematic independence. But this complex linear framework could be said to build in quantum theory from the start. We show that the first two equivalences break, and the third holds, in a framework of generalized, possibly nonlinear, C*-algebras. This uncovers a hierarchy of notions of when (quantum) information is classical.