  A complex frame is a collection of vectors that span $\mathbb{C}^M$ and
define measurements, called intensity measurements, on vectors in
$\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is
to recover a complex vector from its intensity measurements, namely the modulus
of its inner product with these frame vectors. We show that any vector is
uniquely determined (up to a global phase factor) from $4M-4$ generic
measurements. To prove this, we identify the set of frames defining
non-injective measurements with the projection of a real variety and bound its
dimension.
