Exponential precision by reaching a quantum critical point

TL;DR

This paper introduces a quantum metrology protocol that surpasses polynomial scaling, achieving exponential precision advantage by approaching a quantum critical point without crossing it.

Contribution

It demonstrates a novel protocol leveraging quantum criticality to attain exponential scaling of quantum Fisher information, exceeding the Heisenberg limit.

Findings

Achieves exponential scaling of quantum Fisher information near a quantum critical point.

Analytical expressions match numerical simulations for the quantum Fisher information.

Discusses limitations and robustness of the protocol against finite-size effects and decoherence.

Abstract

Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which provides an upper bound to the achievable precision -- with respect to the protocol duration is then of primarily importance to assess its performances. In classical protocols the quantum Fisher information scales linearly with time, while typical quantum-enhanced strategies achieve a quadratic (Heisenberg) or even higher-order polynomial scalings. Here we report a protocol that is capable of surpassing the polynomial scaling, and yields an exponential advantage. Such exponential advantage is achieved by approaching, but without crossing, the critical point of a quantum phase transition of a fully-connected model in the thermodynamic limit. The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in arXiv:2110.04144, which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects. Hence, our findings unveil a novel quantum metrological protocol whose precision scaling goes beyond the paradigmatic Heisenberg limit with respect to the protocol duration.