Quantum Fisher information as a witness of non-Markovianity and criticality in the spin-boson model

TL;DR

This paper investigates how quantum Fisher information can serve as a tool to detect non-Markovian effects and quantum phase transitions in the spin-boson model, providing insights into quantum resources and criticality.

Contribution

It introduces a numerically exact method to analyze quantum Fisher information in the spin-boson model, linking it to entanglement, non-Markovianity, and phase transitions.

Findings

Quantum Fisher information signals the BKT quantum phase transition.

Time-dependent quantum Fisher information reveals non-Markovian effects.

Non-monotonic behavior of Fisher information relates to quantum resources.

Abstract

The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using numerically exact methods applied to a paradigmatic open quantum system, the spin-boson model, we calculate both static and dynamical quantum Fisher information matrix elements with respect to spin-bath couplings and magnetic field strengths. As the spin-bath interaction increases, we first show that the coupling-coupling matrix elements relative to the ground state of the Hamiltonian are linked to the entanglement growth and signal the Berezinskii-Kosterlitz-Thouless quantum phase transition through their non-monotonic behavior. We also point out that the static quantum Fisher information exhibits a non-perturbative behavior in the zero-coupling limit, which we justify with an analytic argument. Furthermore, we demonstrate that the time-dependent matrix elements can reveal non-Markovian effects as well as the transition from the coherent to incoherent regime at the Toulouse point, remaining robust under pure dephasing noise. Non-monotonic signatures of the quantum Fisher information matrix reflect changes in quantum resources such as entanglement and coherence, quantify non-Markovian behavior, and enable criticality-enhanced quantum sensing, thereby shedding light on key features of open quantum systems.