  We give a analytic quantitative relation between Hardy's non-locality and
Bell operator. We find that Hardy's non-locality is a sufficient condition for
violation of Bell inequality, the upper bound of Hardy's non-locality allowed
by information causality just correspond to Tsirelson bound of Bell inequality,
and the upper bound of Hardy's non-locality allowed by the principle of
no-signaling just correspond to the algebraic maximum of Bell operator. Then we
study the Cabello's argument of Hardy's non-locality (a generalization of
Hardy's argument) and find a similar relation between it and violation of Bell
inequality. Finally, we give a simple derivation of the bound of Hardy's
non-locality under the constraint of information causality with the aid of
above derived relation between Hardy's non-locality and Bell operator, this
bound is the main result of a recent work of Ahanj \emph{et al.} [Phys. Rev. A
{\bf81}, 032103(2010)].
