We study stability and uniqueness for the phase

retrieval problem. That is, we ask when is a signal x ∈ R

n

stably and uniquely determined (up to small perturbations), when

one performs phaseless measurements of the form yi = |a

T

i x|

2

(for i = 1, . . . , N), where the vectors ai ∈ R

n

are chosen

independently at random, with each coordinate aij ∈ R being

chosen independently from a fixed sub-Gaussian distribution

D. It is well known that for many common choices of D,

certain ambiguities can arise that prevent x from being uniquely

determined.

In this note we show that for any sub-Gaussian distribution

D, with no additional assumptions, most vectors x cannot lead

to such ambiguities. More precisely, we show stability and

uniqueness for all sets of vectors T ⊂ R

n which are not

too peaky, in the sense that at most a constant fraction of

their mass is concentrated on any one coordinate. The number

of measurements needed to recover x ∈ T depends on the

complexity of T in a natural way, extending previous results

of Eldar and Mendelson [12].