Using adaptiveness and causal superpositions against noise in quantum metrology

TL;DR

This paper establishes new bounds on precision in adaptive quantum metrology, demonstrating asymptotic equivalence with parallel strategies and showing no advantage of causal superpositions in the limit of many channel uses.

Contribution

It provides the first proof of asymptotic equivalence between adaptive and parallel quantum metrology strategies and assesses the limited benefits of causal superpositions.

Findings

New bounds on quantum metrological precision derived

Asymptotic equivalence between adaptive and parallel strategies proven

Causal superpositions do not offer asymptotic advantage

Abstract

We derive new bounds on achievable precision in the most general adaptive quantum metrological scenarios. The bounds are proven to be asymptotically saturable and equivalent to the known parallel scheme bounds in the limit of large number of channel uses. This completely solves a long standing conjecture in the field of quantum metrology on asymptotic equivalence between parallel and adaptive strategies. The new bounds also allow to easily assess the potential benefits of invoking the non-standard causal superposition strategies, for which we prove, similarly to the adaptive case, the lack of asymptotic advantage over the parallel ones.