On the Colbeck-Renner Theorem

TL;DR

This paper refines and clarifies the Colbeck-Renner theorem, demonstrating that no alternative theory compatible with quantum mechanics and free choice can yield better predictions, with a more precise proof and additional assumptions.

Contribution

It provides a more rigorous and detailed formulation and proof of the Colbeck-Renner theorem, clarifying the assumptions involved.

Findings

The theorem confirms the incompatibility of improved predictions with quantum theory under specified assumptions.

Additional technical assumptions were identified and incorporated into the proof.

The proof relies on physically motivated axioms but introduces some assumptions with unclear physical interpretation.

Abstract

In three papers Colbeck and Renner (Nature Communications 2:411, (2011); Phys. Rev. Lett. 108, 150402 (2012); 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.