Quantum metrology with full and fast quantum control

TL;DR

This paper investigates the fundamental limits of quantum parameter estimation with full and fast quantum control, revealing conditions under which Heisenberg scaling can be restored or limited by noise types.

Contribution

It establishes how fast quantum control can recover or enhance quantum metrological precision limits under various noise conditions.

Findings

Fast control restores Heisenberg scaling for certain noise types.

Quantum enhancement is limited to a constant factor for most noise types.

Sequential schemes can outperform parallel entangled schemes without fast control.

Abstract

We establish general limits on how precise a parameter, e.g. frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (~1/N) even when allowing for the full power of fast control. The latter holds both in the single-shot and infinitely-many repetitions scenarios. However, even in this case allowing for fast quantum control helps to increase the improvement factor. Furthermore, for frequency estimation with finite resource we show how a parallel scheme utilizing any fixed number of entangled qubits but no fast quantum control can be outperformed by a simple, easily implementable, sequential scheme which only requires entanglement between one sensing and one auxiliary qubit.