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Precision measurement of magnetic fields is an important goal for fundamentalscience and practical sensing technology. Sensitive detection of a vectormagnetic field is a crucial issue in quantum magnetometry, it remains achallenge to estimate a vector DC magnetic field with high efficiency and highprecision. Here, we propose a general protocol for quantum vector DCmagnetometry via selective phase accumulation of both non-entangled andentangled quantum probes. Based upon the Ramsey interferometry, our protocolmay achieve selective phase accumulation of only one magnetic field componentby inserting well-designed pulse sequence. In the parallel scheme, threeparallel quantum interferometries are utilized to estimate three magnetic fieldcomponents independently.In the sequential scheme, by applying a pulse sequencealong different directions, three magnetic field components can be estimatedsimultaneously via only one quantum interferometry. In particular, if the inputstate is an entangled state such as the Greenberger-Horne-Zeilinger state, themeasurement precisions of all three components may approach the Heisenberglimit. Our study not only develops a general protocol for measuring vectormagnetic fields via quantum probes, but also provides a feasible way to achieveHeisenberg-limited multi-parameter estimation via many-body quantumentanglement.

Quantum Vector DC Magnetometry via Selective Phase Accumulation