erm...not quite...you technically run into "knowledge about each element of a system versus knowledge about the entire system" tradeoffs. Although...you CAN partially bypass "no quantum Xerox" if you have a large sample. It's the principle used in error-correction for quantum computers.

Take a laser. point it at a perfect polarizer of unknown orientation, and fire a pulse. Send the photons that get through one by one through filters of known orientation as you hone in convergently (hehe) on the orientation of the first polarizer.

There is a tiny chance that you won't have a remotely correct value, and you never get exact with a finite sample, but you can probably do well enough to satisfy the typical engineer with only a "couple hundred" photons.