Entanglement between a qubit and the environment in the spin-boson model

Abstract

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 $\alpha$, the strength of the ohmic coupling to the environment, and $\epsilon$, the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For $\epsilon =0$, the entanglement increases monotonically with $\alpha$, until it becomes maximal for $\alpha \lim 1^{-}$. For fixed $\epsilon >0$, the entanglement is a maximum as a function of $\alpha$ for a value, $\alpha ={\alpha }_M<1$.

4 pages, 3 figures. Shortened version restricted to groundstate entanglement