  We prove new results about the robustness of well-known convex noise-blind
optimization formulations for the reconstruction of low-rank matrices from
underdetermined linear measurements. Our results are applicable for symmetric
rank-one measurements as used in a formulation of the phase retrieval problem.
  We obtain these results by establishing that with high probability rank-one
measurement operators defined by i.i.d. Gaussian vectors exhibit the so-called
Schatten-1 quotient property, which corresponds to a lower bound for the
inradius of their image of the nuclear norm (Schatten-1) unit ball.
  We complement our analysis by numerical experiments comparing the solutions
of noise-blind and noise-aware formulations. These experiments confirm that
noise-blind optimization methods exhibit comparable robustness to noise-aware
formulations.
  Keywords: low-rank matrix recovery, phase retrieval, quotient property,
noise-blind, robustness, nuclear norm minimization
