Ensemble based quantum metrology

The field of quantum metrology promises measurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed the precision achieved is supposed to scale more favourably with the resources employed, such as system size and the time required. Here we consider measurement of magnetic field strength using an ensemble of spins, and we identify a third essential resource: the initial system polarisation, i.e. the low entropy of the original state. We find that performance depends crucially on the form of decoherence present; for a plausible dephasing model, we describe a quantum strategy which can indeed beat the standard quantum limit.