Quantum limits of thermometry

The precision of typical thermometers consisting of N particles scales as similar to 1/root N. For high-precision thermometry and thermometric standards, this presents an important theoretical noise floor. Here it is demonstrated that thermometry may be mapped onto the problem of phase estimation, and using techniques from optimal phase estimation, it follows that the scaling of the precision of a thermometer may in principle be improved to similar to 1/N, representing a Heisenberg limit to thermometry.