Magnetic Field Measurement with Heisenberg Limit Based on Solid Spin NOON State

The maximum entangled number state (NOON state) can improve the sensitivity of physical quantity measurement to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid spin NOON state is investigated. Based on the tunable effective coupling coefficient, we propose a generation scheme of the three-spin NOON state, i.e, the Greenberger–Horne–Zeilinger (GHZ) state, and discussed the measurement resolution reduction due to decoherence. It is unnecessary to entangle spins as many as possible when decoherence exists. In practice, defect spins in diamond and ³¹P donors with long coherence time can be applied with current techniques in the nano-scaled high resolution magnetic measurement.