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

TL;DR

This paper explains the Tsirelson bound in quantum mechanics as a consequence of conservation principles related to no preferred reference frames, paralleling the foundational approach of special relativity.

Contribution

It derives the Tsirelson bound from conservation principles and no preferred reference frame, providing a principle-based explanation aligned with the structure of special relativity.

Findings

Quantum correlations are derived from conservation per NPRF.

The Tsirelson bound is linked to no preferred reference frame.

Quantum states corresponding to Bell basis are explained through this principle.

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."