  The aim of this paper is to study the stability of the $\ell_1$ minimization
for the compressive phase retrieval and to extend the instance-optimality in
compressed sensing to the real phase retrieval setting. We first show that the
$m={\mathcal O}(k\log(N/k))$ measurements is enough to guarantee the $\ell_1$
minimization to recover $k$-sparse signals stably provided the measurement
matrix $A$ satisfies the strong RIP property. We second investigate the
phaseless instance-optimality with presenting a null space property of the
measurement matrix $A$ under which there exists a decoder $\Delta$ so that the
phaseless instance-optimality holds. We use the result to study the phaseless
instance-optimality for the $\ell_1$ norm. The results build a parallel for
compressive phase retrieval with the classical compressive sensing.
