  A universal programmable detector is a device that can be tuned to perform
any desired measurement on a given quantum system, by changing the state of an
ancilla. With a finite dimension d for the ancilla only approximate universal
programmability is possible, with "size" d=f(1/e) increasing function of the
"accuracy" 1/e. In this letter we show that, much better than the exponential
size known in the literature, one can achieve polynomial size. An explicit
example with linear size is also presented. Finally, we show that for covariant
measurements exact programmability is feasible.
