Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

TL;DR

This paper investigates how local quantum uncertainty (LQU) can serve as a lower bound for quantum Fisher information (QFI) in two coupled two-level systems within non-Markovian environments, highlighting conditions where LQU effectively predicts measurement precision.

Contribution

It establishes a direct relation between LQU and QFI in open quantum systems with non-Markovian environments, especially when systems are uncoupled or in Bell states, extending previous bounds.

Findings

QFI decay is mitigated by increasing coupling strength or non-Markovianity.

LQU can bound QFI effectively when systems are uncoupled or in Bell states.

QFI is independent of the phase parameter in the studied open systems.

Abstract

Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cram\'er-Rao inequality. When the quantum state satisfies the von Neumann-Landau equation, the local quantum uncertainty (LQU), as a kind of quantum correlation, present in a bipartite mixed state guarantees a lower bound on QFI in the optimal phase estimation protocol [Phys. Rev. Lett. 110 (2013) 240402]. However, in the open quantum systems, there is not an explicit relation between LQU and QFI generally. In this paper, we study the relation between LQU and QFI in open systems which is composed of two interacting two-level systems coupled to independent non-Markovian environments with the entangled initial state embedded by a phase parameter $\theta$. The analytical calculations show that the QFI does't depend on the phase parameter $\theta$, and its decay can be restrained through enhancing the coupling strength or non-Markovianity. Meanwhile, the LQU is related to the phase parameter $\theta$ and shows plentiful phenomena. In particular, we find that the LQU can well bound the QFI when the coupling between the two systems is switched off or the initial state is Bell state.