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arXiv:1509.08498 · Journal of Mathematical Physics

On the Colbeck–Renner theorem

Klaas Landsman

Published Dec 1, 2015• 8 citations
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Abstract

In three papers, Colbeck and Renner [Nat. Commun. 2, 411 (2011); Phys. Rev. Lett. 108, 150402 (2012); e-print arXiv:1208.4123] argued that “no alternative theory compatible with quantum theory and satisfying the freedom of choice assumption can give improved predictions.” We give a more precise version of the formulation and proof of this remarkable claim. Our proof broadly follows theirs, which relies on physically well motivated axioms, but to fill in some crucial details, certain technical assumptions have had to be added, whose physical status seems somewhat obscure.

DOI
10.1063/1.4936556

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In three papers, Colbeck and Renner [Nat. Commun. 2, 411 (2011); Phys. Rev. Lett. 108, 150402 (2012); e-print arXiv:1208.4123] argued that “no alternative theory compatible with quantum theory and satisfying the freedom of choice assumption can give improved predictions.” We give a more precise version of the formulation and proof of this remarkable claim. Our proof broadly follows theirs, which relies on physically well motivated axioms, but to fill in some crucial details, certain technical assumptions have had to be added, whose physical status seems somewhat obscure.
In this thesis a recent claim by Roger Colbeck and Renato Renner is reviewed [18]. This claim concerns the completeness of quantum mechanics. Colbeck and Renner state that no theory can be constructed that is compatible with quantum mechanics, and gives more detailed predictions through supplemental variables added to the description of the state of a system. Their only assumption is that measurement settings can be choosen freely. We will argue that their result is for the most part valid and interesting, but the freedom assumption is not so innocent as it is presented, and parts of the result need to be clarified. Therefore, we will present a reformulation of the result. In our formulation the result is a no-go theorem for hidden variable theories satisfying Parameter Independence. This is a generalization of Bell’s theorem. Performed in the period 01-11-2012 14-08-2012
In a series of papers Colbeck and Renner (2011, 2015a,b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Landsman (2015) and Leegwater (2016) I highlight the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I show that the assumption is quite crucial to the proof of the claim and argue that it is unwarranted. I further discuss a possible validation for a restricted version of this assumption that is based on considerations of measurement processes. I argue that also this restricted version is unsatisfactory.
In a series of papers Colbeck and Renner claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer, Landsman and Leegwater, I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.
In a series of papers Colbeck and Renner (2011, 2015a, 2015b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer (2014), Landsman (2015) and Leegwater (2016), I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.