Dynamical phase transitions as a resource for quantum enhanced metrology

TL;DR

This paper links dynamical phase transitions in open quantum systems to enhanced quantum metrology, showing that near such transitions, the quantum Fisher information scales quadratically with time, enabling Heisenberg-limited precision.

Contribution

It establishes a direct relation between dynamical phase transitions and quantum Fisher information scaling, proposing a scheme for quantum enhanced phase estimation leveraging this phenomenon.

Findings

QFI becomes quadratic in time at first-order dynamical phase transitions

Enhanced scaling of QFI is due to divergence of observable variance at the transition

Proposes a scheme for quantum enhanced phase estimation using emitted photons

Abstract

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. "Heisenberg scaling"). In fact, the QFI is identical to the variance of the dynamical observable that characterises the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification allows to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realisation of these ideas, we describe a theoretical scheme for quantum enhanced phase estimation using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.