Simulating all quantum measurements using only projective measurements
  and postselection
We report an alternative scheme for implementing generalized quantum
measurements that does not require the usage of auxiliary system. Our method
utilizes solely: (a) classical randomness and post-processing, (b) projective
measurements on a relevant quantum system and (c) postselection on
non-observing certain outcomes. The scheme implements arbitrary quantum
measurement in dimension $d$ with the optimal success probability $1/d$. We
apply our results to bound the relative power of projective and generalised
measurements for unambiguous state discrimination. Finally, we test our scheme
experimentally on IBM's quantum processor. Interestingly, due to noise involved
in the implementation of entangling gates, the quality with which our scheme
implements generalized qubit measurements outperforms the standard construction
using the auxiliary system.
Michał Oszmaniec Filip B. Maciejewski Zbigniew Puchała