  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, $\alpha = \alpha_M < 1$.
