  We study quantum transport in ballistic $s_\pm$-wave superconductors where
coupling between the two bands is included, and apply our model to three
possible probes for detecting the internal phase shift of such a pairing state:
tunneling spectroscopy in a N$|s_\pm$-wave junction, crossed Andreev reflection
in a two-lead N$|s_\pm$-wave$|$N system, and Josephson current in a
s-wave$|$I$|s_\pm$-wave Josephson junction. Whereas the first two probes are
insensitive to the superconducting phase in the absence of interband coupling,
the Josephson effect is intrinsically phase-dependent, and is moreover shown to
be relatively insensitive to the strength of the interband coupling. Focusing
on the Josephson current, we find a 0-$\pi$ transition as a function of the
ratio of effective barrier transparency for the two bands, as well as a similar
phase-shift effect as a function of temperature. An essential feature of this
$s_\pm$-wave model is non-sinusoidality of the current-phase relation, and we
compute the dependence of the critical current on an external magnetic field,
showing how this feature may be experimentally observable for this system. We
also comment on the possible experimental detection of the phase shift effects
in $s_\pm$-wave superconductors.
