Quantum Metrology in Noisy Environments
The best precision achievable in a phase estimation problem is bounded by the so called Heisenberg limit. In principle, this limit can be reached by using maximally entangled states and would lead to an improvement over the precision achievable with product states (standard quantum limit) equal to 1/sqrt(n), where n is the number of subsystems.
We will discuss how this result is affected by the presence of noise and analyze optimal bounds for precision spectroscopy in noisy environments. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under Markovian decoherence fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite band-width ephasing environment, we show that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states but 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 that goes beyond specific models and, as a result, provides a novel metrological bound that we brand "Zeno bound". These results emphasize the usefulness of quantum correlated states for metrology in a range of realistic experimental conditions.