  A central long standing prediction of the theory of fractional quantum Hall
(FQH) states that it is a topological fluid whose elementary excitations are
vortices with fractional charge and fractional statistics. Yet, the unambiguous
experimental detection of this fundamental property, that the vortices have
fractional statistics, has remained an open challenge. Here we propose a
three-terminal ``T-junction'' as an experimental setup for the direct and
independent measurement of the fractional charge and statistics of fractional
quantum Hall quasiparticles via cross current noise measurements. We present a
non-equilibrium calculation of the quantum noise in the T-junction setup for
FQH Jain states. We show that the cross current correlation (noise) can be
written in a simple form, a sum of two terms, which reflects the braiding
properties of the quasiparticles: the statistics dependence captured in a
factor of $\cos\theta$ in one of two contributions. Through analyzing these two
contributions for different parameter ranges that are experimentally relevant,
we demonstrate that the noise at finite temperature reveals signatures of
generalized exclusion principles, fractional exchange statistics and fractional
charge. We also predict that the vortices of Laughlin states exhibit a
``bunching'' effect, while higher states in the Jain sequences exhibit an
``anti-bunching'' effect.
