Quantum measurement of spins and magnets, and the classical limit of PR-boxes

TL;DR

The paper explores the classical limit of quantum correlations, demonstrating that macroscopic measurements cannot reveal Alice's measurement choices and deriving Tsirelson's bound from physical assumptions about compatibility and no signaling.

Contribution

It shows that even with large ensembles and strong correlations, measurement choices remain hidden and derives Tsirelson's bound from macroscopic measurement compatibility.

Findings

Large ensembles do not allow reading measurement choices from magnetic moments.

Tsirelson's bound follows from assumptions of measurement compatibility and no signaling.

Macroscopic limits preserve the classicality of measurement outcomes.

Abstract

When Alice measures all her spin-$\half$ of a large ensemble of $N$ singlets, all along the same direction $\vec a$, she prepares at a distance an ensemble of spins for Bob which, because of statistical fluctuations, have a magnetic moment of the order $\sqrt{N}$. By making $N$ large enough, this magnetic moment can be made arbitrarily large. We show that, nevertheless, Bob can't read out of this large magnetic moment Alice's choice of measurement direction $\vec a$. We also consider stronger than quantum correlations and show that Tsirelson's bound follows from the physical assumption that in the macroscopic limit all measurements are compatible and that this should not lead to signaling.