  It is well known that any projective measurement can be decomposed into a
sequence of weak measurements, which cause only small changes to the state.
Similar constructions for generalized measurements, however, have relied on the
use of an ancilla system. We show that any generalized measurement can be
decomposed into a sequence of weak measurements without the use of an ancilla,
and give an explicit construction for these weak measurements. The measurement
procedure has the structure of a random walk along a curve in state space, with
the measurement ending when one of the end points is reached. This shows that
any measurement can be generated by weak measurements, and hence that weak
measurements are universal. This may have important applications to the theory
of entanglement.
