  Generalized quantum measurements (POVMs or POMs) are important for optimally
extracting information for quantum communication and computation. The standard
realization via the Neumark extension requires extensive resources in the form
of operations in an extended Hilbert space. For an arbitrary measurement, we
show how to construct a binary search tree with a depth logarithmic in the
number of possible outcomes. This could be implemented experimentally by
coupling the measured quantum system to a probe qubit which is measured, and
then iterating.
