Quantum Metrology in Non-Markovian Environments

TLDR

Under general Markovian noise, any small amount of noise restores standard quantum limit scaling, contrasting with the non‑Markovian case. The study examines precision limits for local phase estimation under general non‑Markovian phase noise. An exactly solvable finite‑bandwidth dephasing model shows that non‑Markovian dynamics allow quantum‑correlated states to outperform uncorrelated strategies with the same resources. Non‑Markovian noise breaks the equivalence between product and entangled states, enabling correlated states to surpass the standard quantum limit—though not reaching Heisenberg scaling—due to coherent system‑environment dynamics, a result that holds generally beyond specific models.

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.