Typically, the system is composed of many particles, and the Hamiltonian is a sum of single-particle terms where
[1][11] One example of note is the use of the NOON state in a Mach–Zehnder interferometer to perform accurate phase measurements.
In atomic ensembles, spin squeezed states can be used for phase measurements.
An important application of particular note is the detection of gravitational radiation in projects such as LIGO or the Virgo interferometer, where high-precision measurements must be made for the relative distance between two widely separated masses.
However, the measurements described by quantum metrology are currently not used in this setting, being difficult to implement.
Furthermore, there are other sources of noise affecting the detection of gravitational waves which must be overcome first.
[13] A central question of quantum metrology is how the precision, i.e., the variance of the parameter estimation, scales with the number of particles.
Shot-noise limit is known to be asymptotically achievable using coherent states and homodyne detection.
[14] Quantum metrology can reach the Heisenberg limit given by However, if uncorrelated local noise is present, then for large particle numbers the scaling of the precision returns to shot-noise scaling
It has been shown that quantum entanglement is needed to outperform classical interferometry in magnetometry with a fully polarized ensemble of spins.
[17] It has been proved that a similar relation is generally valid for any linear interferometer, independent of the details of the scheme.
[19][20] Additionally, entanglement in multiple degrees of freedom of quantum systems (known as "hyperentanglement"), can be used to enhance precision, with enhancement arising from entanglement in each degree of freedom.