Working Paper Article Version 1 This version is not peer-reviewed

Why the Tsirelson Bound? Bub's Question and Fuchs' Desideratum

Version 1 : Received: 30 June 2019 / Approved: 2 July 2019 / Online: 2 July 2019 (04:24:45 CEST)

A peer-reviewed article of this Preprint also exists.

Stuckey, W.; Silberstein, M.; McDevitt, T.; Kohler, I. Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum. Entropy 2019, 21, 692. Stuckey, W.; Silberstein, M.; McDevitt, T.; Kohler, I. Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum. Entropy 2019, 21, 692.

Journal reference: Entropy 2019, 21, 692
DOI: 10.3390/e21070692

Abstract

To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF."

Subject Areas

Tsirelson bound; Bell-CHSH inequality; superquantum correlations; quantum information theory

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