This paper proposes a scheme to implement general quantum measurements (POVMs) in dimension *d* using only classical resources and a single ancillary qubit. The method involves a probabilistic implementation of *d*-outcome measurements followed by postselection. The authors conjecture that the success probability is greater than a constant independent of *d* for all POVMs, implying the possibility of realizing arbitrary nonadaptive quantum measurement protocols with constant overhead. This conjecture is shown to hold for typical rank-one Haar-random POVMs and supported by numerical computations on various POVMs, including SIC-POVMs up to dimension 1299. The scheme is argued to be experimentally favorable due to lower noise compounding compared to standard Naimark's dilation.

Tanmay Singal, Filip B. Maciejewski, Michał Oszmaniec