  We disentangle all the individual degrees of freedom in the quantum impurity
problem to deconstruct the Kondo singlet, both in real and energy space, by
studying the contribution of each individual free electron eigenstate. This is
a problem of two spins coupled to a bath, where the bath is formed by the
remaining conduction electrons. Being a mixed state, we resort to the
"concurrence" to quantify entanglement. We identify "projected natural
orbitals" that allow us to individualize a single-particle electronic wave
function that is responsible of more than $90\%$ of the impurity screening. In
the weak coupling regime, the impurity is entangled to an electron at the Fermi
level, while in the strong coupling regime, the impurity counterintuitively
entangles mostly with the high energy electrons and disentangles completely
from the low-energy states carving a "hole" around the Fermi level. This
enables one to use concurrence as a pseudo order parameter to compute the
characteristic "size" of the Kondo cloud, beyond which electrons are are weakly
correlated to the impurity and are dominated by the physics of the boundary.
