  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.
