Simulating all quantum measurements using only projective measurements and postselection

TL;DR

This paper introduces a new method for implementing generalized quantum measurements using only projective measurements, postselection, and classical randomness, achieving optimal success probability without auxiliary systems.

Contribution

The authors present an auxiliary-system-free scheme for generalized quantum measurements, with experimental validation on IBM's quantum processor, outperforming standard methods under noise.

Findings

Achieves optimal success probability of 1/d for dimension d

Experimental implementation on IBM quantum processor

Outperforms standard auxiliary-system methods under noise

Abstract

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.