The short answer is that the circuit drawer does not have a way to label "sections".
However, you can pass an arbitrary
matplotlib.axes.Axes to the Matplotlib circuit drawer (only to that circuit drawer) where you can set and position your labels by hand. For your particular case, it looks something like this:
from matplotlib.pyplot import figure
fig = figure()
ax = fig.add_subplot()
height = 0.8
ax.text(-0.9, height, 'entanglement', size=14)
ax.text(2.5, height, 'init', size=14)
ax.text(4.5, height, 'transfer of\namplitudes', size=14)
ax.text(7, height, 'measurement', size=14)
You might have to adapt the
y numbers (the first two parameters for
text) to readjust their position.