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.
7 + 3 pages, 1 + 2 figures, 1 + 0 tables, comments and suggestions are welcome; v2: improved narrative in the main text, proofs of some technical details were moved to the appendix; v3: changed title, improved narrative in the main text, corrected typos in Appendix (matrix elements of tetrahedral measurement)