Quantum Metrology in Non-Markovian Environments

TL;DR

This paper investigates how non-Markovian noise affects quantum metrology, showing that non-Markovian dynamics can enable quantum states to outperform uncorrelated states, unlike in Markovian environments.

Contribution

It demonstrates that non-Markovian effects break the equivalence of product and entangled states in quantum metrology, allowing quantum advantage under realistic noise conditions.

Findings

Non-Markovian dynamics enable quantum states to surpass the standard quantum limit.

The advantage is due to coherent system-environment interactions.

Scaling surpasses the SQL but does not reach Heisenberg limit.

Abstract

We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.