Quantum criticality as a resource for quantum estimation

We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if $L$ denotes the size of a system and $\lambda$ is the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order $1∕L$ may be achieved in the estimation of $\lambda$ at the critical point compared to the noncritical case. We show that analog results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).