Quantum metrology with one auxiliary particle in a correlated bath and its quantum simulation

In realistic metrology, entangled probes are more sensitive to noise, especially for a correlated environment. The precision of parameter estimation with entangled probes is even lower than that of the unentangled ones in a correlated environment. In this paper we propose a measurement scheme with only one auxiliary qubit, which can selectively offset the impact of environmental noise under this situation. We analyze the estimation precision of our scheme and find out that it approaches the Heisenberg limit when prepared in a proper auxiliary state. We further discuss employing auxiliary states to improve the precision of measurement in other environment models such as a partially correlated environment. In order to verify our scheme, we apply a recently developed quantum algorithm to simulate the quantum dynamics of our proposal and show that it outperforms the other proposals with less resources.