Quantum criticality as a resource for quantum estimation

TL;DR

This paper explores how quantum critical systems can enhance the precision of parameter estimation, demonstrating that near critical points, estimation accuracy can significantly improve, with potential applications in classical and quantum phase transition measurements.

Contribution

It establishes the fundamental quantum limits for parameter estimation at quantum critical points and shows a potential 1/L precision improvement, supported by a fermionic model example.

Findings

Precision improves by order 1/L at critical points.

Similar results apply to temperature estimation in classical phase transitions.

Illustrated with a fermion tight-binding (BCS) model.

Abstract

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 non-critical case. We show that analogue 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).