Quantum Limits of Thermometry

The precision of typical thermometers consisting of $N$ particles is shot noise limited, improving as $\sim1/\sqrt{N}$. 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 $\sim1/N$, representing a Heisenberg limit to thermometry.