Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme

Understand

The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology.

• Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field with entangled probe states under the parallel scheme remains unknown.
• Here we present the ultimate lower bound for the sum of arbitrarily weighted variances in the estimation of all three components of a magnetic field under the parallel scheme and show that this lower bound can be achieved for sufficiently large N.
• The optimal entangled probe state that achieves the ultimate precision is also explicitly constructed.