Enhancement of Frequency Estimation by Spatially Correlated Environments

TL;DR

This paper demonstrates that spatially correlated environments can enhance frequency estimation precision in quantum metrology beyond traditional limits by exploiting decoherence-free subspaces and nonlocal dynamics.

Contribution

It introduces the impact of spatially correlated noise on quantum metrology, showing potential for surpassing Zeno scaling and achieving Heisenberg scaling.

Findings

Spatially correlated environments enable improved frequency estimation.

Decoherence-free subspaces can be exploited for better precision.

Heisenberg scaling is achievable with nonlocal, non-semigroup dynamics.

Abstract

In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estimation. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate quantum improvement. One of the most destructive decoherence-type noise is uncorrelated Markovian noise which commutes with the parameter-encoding Hamiltonian and is modelled as a semigroup dynamics, for which the quantum improvement is constrained to a constant factor. It has been shown [Phys. Rev. Lett. \textbf{109}, 233601 (2012)] that when the noisy time evolution is governed by a local and non-semigroup dynamics (e.g., induced by an uncorrelated non-Markovian dephasing), emerging the Zeno regime at short times can result in the Zeno scaling in the precision. Here, by considering the impact of the correlated noise in metrology, we show that spatially correlated environments which lead to a nonlocal and non-semigroup dynamics can improve the precision of a noisy frequency measurement beyond the Zeno scaling. In particular, it is demonstrated that one can find decoherence-free subspaces and subsequently achieve the Heisenberg precision scaling for an approximated dynamics induced by spatially correlated environments.