  Weak-value amplification (WVA) provides a way for amplified detection of a
tiny physical signal at the expense of a lower detection probability. Despite
this trade-off, due to its robustness against certain types of noise, WVA has
advantages over conventional measurements in precision metrology. Moreover, it
has been shown that WVA-based metrology can reach the Heisenberg-limit using
entangled resources, but preparing macroscopic entangled resources remains
challenging. Here we demonstrate a novel WVA scheme based on iterative
interactions, achieving the Heisenberg-limited precision scaling without
resorting to entanglement. This indicates that the perceived advantages of the
entanglement-assisted WVA are in fact due to iterative interactions between
each particle of an entangled system and a meter, rather than coming from the
entanglement itself. Our work opens a practical pathway for achieving the
Heisenberg-limited WVA without using fragile and experimentally-demanding
entangled resources.
