# Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system

**Authors:** Karyn Le Hur  
**arXiv:** [0711.2301](https://arxiv.org/abs/0711.2301)  
**Date:** 2007-11-14  
**Summary page:** https://www.summarizepaper.com/en/paper/0711.2301v3/

## Key points

- Study by Karyn Le Hur on entanglement entropy in various contexts
- Focus on investigating entanglement entropy within the spin-boson model framework
- Crucial role of entanglement entropy in unifying entanglement, decoherence, and quantum phase transitions
- Demonstration of universal scalings of entanglement entropy through exact analytical derivations and Numerical Renormalization Group arguments
- Comparisons between entanglement properties in the quantum Ising model and the Dicke model
- Potential for measuring entanglement entropy using charge qubits exposed to electromagnetic noise

## Summary

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The study conducted by Karyn Le Hur, titled "Entanglement Entropy, Decoherence, and Quantum Phase Transition of a Dissipative Two-Level System," explores the concept of entanglement entropy in various contexts ranging from black hole physics to quantum information theory. The research focuses on investigating entanglement entropy within the framework of the spin-boson model, which involves a qubit interacting with harmonic oscillators representing the environment responsible for decoherence and dissipation. The analysis reveals that entanglement entropy plays a crucial role in unifying the entanglement between the spin and its environment, as well as decoherence processes and quantum phase transitions. Through exact analytical derivations supported by Numerical Renormalization Group arguments for both ohmic and subohmic bosonic baths, it is demonstrated that entanglement entropy follows universal scalings. Comparisons are also drawn between entanglement properties in the quantum Ising model and the Dicke model to further elucidate these findings. Moreover, this study highlights the potential for measuring entanglement entropy using charge qubits exposed to electromagnetic noise as a means of empirically confirming its existence. Overall, this comprehensive investigation contributes valuable insights into understanding the intricate interplay between entanglement, decoherence, and quantum phase transitions within dissipative two-level systems.