Researchers reveal entanglement witness in spin-boson model via Fisher information calculations

Understanding how systems interact with their environment is fundamental to quantum physics, and recent research delves into the subtle signals that reveal the nature of these interactions. Researchers, including D. Parlato, G. Di Bello, and F. Pavan from the University of Naples Federico II, investigate these signals using a concept called quantum Fisher information, a measure of how sensitive a system is to changes in its parameters. Applying this approach to the spin-boson model, a standard example in quantum physics, the team demonstrates that the quantum Fisher information effectively identifies both entanglement and critical points in a system, as well as revealing when a system’s behaviour transitions from predictable to chaotic. This work provides a new tool for characterising open quantum systems and could lead to improvements in quantum sensing technologies by pinpointing conditions where sensitivity is maximised.

Quantum Fisher Information, Spin-Boson Model Calculations

This document provides extensive supporting information for a research paper investigating how the Quantum Fisher Information (QFI) can be used to detect both quantum phase transitions and non-Markovian behavior in the spin-boson model. It expands on the main text by detailing the mathematical foundations of the calculations, presenting additional data analysis of the QFI elements, and verifying the reliability of the estimation methods for the critical coupling.

The document examines static QFI elements, quantifying the system’s sensitivity to variations in spin-bath coupling and energy difference. Results show that sensitivity to energy difference diminishes with weak spin-bath coupling, while both elements exhibit peak positions consistent with the main findings. Researchers accurately estimated the critical coupling, αc = 1. 03 ±0. 03, consistent with established literature. A comparison with the Lindblad master equation, an analytical approximation, reveals limitations in capturing the full system dynamics, particularly non-Markovian effects.

Robustness checks, including the comparison with the Lindblad approximation and the critical coupling estimation, demonstrate the reliability of the methods. This research improves understanding of open quantum systems, provides new tools for quantum control, and has potential applications in quantum technologies.

Fisher Information Signals Quantum Entanglement and Transitions

Researchers have achieved a significant breakthrough in understanding open quantum systems using the spin-boson model. Their work demonstrates how the Fisher information, a key quantity for parameter estimation and sensing, reveals crucial details about quantum phase transitions and non-Markovian dynamics. The team employed advanced tensor-network techniques to calculate the Fisher information with unprecedented accuracy, surpassing limitations of previous methods.

Experiments revealed that the Fisher information matrix elements exhibit non-monotonic behavior, serving as a genuine witness of bipartite entanglement and the Berezinskii-Kosterlitz-Thouless phase transition. Specifically, the coupling-coupling matrix elements relative to the ground state display this behavior, signaling changes in entanglement as the system approaches a critical point. Furthermore, time-dependent matrix elements reveal non-Markovian effects, indicating a departure from standard assumptions about memoryless dynamics, and pinpoint the transition from coherent to incoherent behavior.

The data confirms that the Fisher information exhibits a pronounced peak at strong coupling, meaning the system becomes increasingly sensitive to variations in the interaction strength. Notably, as the magnetic field approaches zero, the peak of the Fisher information shifts and becomes sharper, diverging at a critical coupling of αc = 1. 03 ±0. 03, consistent with established literature values. This allows for accurate determination of the critical strength of the quantum phase transition.

Researchers found that the maxima of the Fisher information correspond to the inflection points of the spin polarization, marking regions of high sensitivity for both static and dynamic properties. Interestingly, in the ultra-weak coupling regime, the Fisher information diverges as 1/α, implying very high state sensitivity for small interactions, though this sensitivity rapidly decreases as the coupling increases. This behavior is linked to an increasing ground state von Neumann entropy, indicating that as the spin entangles more with the bath, its sensitivity decreases. Even under weak dephasing, the system retains high sensitivity near the critical point, demonstrating the robustness of these findings. These results provide new insights into the behavior of open quantum systems and pave the way for improved sensing technologies and a deeper understanding of quantum dynamics.

Fisher Information Signals Entanglement and Phase Transitions

This research investigates the Fisher information, a key quantity for understanding precision in measurements and the susceptibility of systems to change, within the spin-boson model. By calculating how the Fisher information changes with variations in spin-bath coupling and magnetic field strength, the team reveals connections between this information and crucial physical properties of the system. The results demonstrate that specific elements of the Fisher information matrix accurately signal changes in entanglement and coherence, and can pinpoint the critical point of a phase transition.

Furthermore, the study shows that time-dependent elements of the Fisher information can reveal how a system transitions from predictable to unpredictable behavior, and identify non-Markovian effects. The authors also find that the Fisher information exhibits a characteristic behavior, decreasing with increasing spin-bath coupling, which is linked to increasing entanglement between the spin and its environment, and can be used to estimate the critical coupling strength of the system.

Future research could explore the applicability of these findings to more complex systems and investigate how the Fisher information can be used to optimize sensing and control in quantum technologies.