Bounding Quantum Advantages in Postselected Metrology

TL;DR

This paper establishes fundamental bounds on quantum advantages in postselected metrology, showing that enhanced precision is limited by these bounds even with quantum resources, and introduces schemes to reach these limits.

Contribution

It derives bounds on quantum advantages in postselected metrology, connecting weak value optimization with geometric phase, and proposes schemes to saturate these bounds.

Findings

Quantum advantages are bounded regardless of quantum resources.

A scheme that saturates the bound yields anomalously large precision.

Positive quasiprobability distributions can achieve advantages traditionally attributed to negativity.

Abstract

Weak value amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. Here we derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Usually, negative quasiprobabilities are considered essential in enabling postselection to increase precision beyond standard optimized values. In contrast, we prove that these advantages can indeed be achieved with positive quasiprobability distribution. We also provide an optimal metrological scheme using three level non-degenerate quantum system.