Entanglement between a qubit and the environment in the spin-boson model
Theo A. Costi, Ross H. McKenzie · Physical Review A · 2003
The quantitative description of the quantum entanglement between a qubit and its environment is considered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin is calculated as a function of $\ensuremath{\alpha},$ the strength of the ohmic coupling to the environment, and $\ensuremath{\varepsilon},$ the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For $\ensuremath{\varepsilon}=0,$ the entanglement increases monotonically with $\ensuremath{\alpha},$ until it becomes maximal for $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}{1}^{\ensuremath{-}}.$ For fixed $\ensuremath{\varepsilon}>0,$ the entanglement is a maximum as a function of $\ensuremath{\alpha}$ for a value, $\ensuremath{\alpha}={\ensuremath{\alpha}}_{M}<1.$