Fundamental Scaling Limit in Critical Quantum Metrology

TL;DR

This paper establishes a fundamental time-dependent scaling limit in critical quantum metrology, linking the quantum Fisher information's exponential growth to the system's topological winding number, even under dissipation.

Contribution

It introduces a fundamental scaling bound based on the winding number and constructs a control scheme to achieve optimal exponential scaling in critical quantum metrology.

Findings

Quantum Fisher information can scale exponentially with time.

Winding number determines the scaling bound.

Exponential scaling persists without reaching criticality or with thermal dissipation.

Abstract

Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution time. To address this challenge, we establish a fundamental scaling limit of critical quantum metrology with respect to the total evolution time. We find that the winding number of the system's phase space trajectory determines the scaling bound of quantum Fisher information. Furthermore, we demonstrate that the exponential scaling of the quantum Fisher information can be obtained, and for this, it is necessary to increase the winding number by the total evolution time. We explicitly construct a time-dependent control to achieve optimal scaling from a simple on-off scheme depending on the system's phase and discuss its topological nature. We highlight that such an exponential scaling of quantum Fisher information remains valid even without reaching the critical point and in the presence of thermal dissipation, albeit with a decreased exponent.