The worst violation of Bell's inequality for $n$ qbits is of size $2^{ \frac{ n-1}{ 2}}$ and it is obtained by a specific operator acting on a specific state. We show, to the contrary, that for a vast majority of Bell operators the worst violation is bounded by $O((n\log n)^{ { 1/2}})$, below experimental detection. With respect to the extremal operators, introduced by Werner and Wolf [Phys. Rev. A 64, 032112 (2001)], we show that a large majority of them have a norm bounded by $O(n^{ { 1/2}})$.
Categories: quant-ph