The goal of quantum metrology is the precise estimation of parameters using quantum properties such as entanglement. This estimation usually consists of three steps: state preparation, time evolution during which information of the parameters is encoded in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity. Assume that we have two axes, and our aim is to estimate the relative angle between them. Our results reveal that the use of Markvoian collective dephasing to estimate the relative angle between the two directions affords Heisenberg-limited sensitivity. Moreover, our scheme based on Markvoian collective dephasing is robust against environmental noise, and it is possible to achieve the Heisenberg limit even under the effect of independent dephasing. Our counterintuitive results showing that the sensitivity is improved by using the decoherence pave the way to novel applications in quantum metrology.
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