  We explore entanglement loss along renormalization group trajectories as a
basic quantum information property underlying their irreversibility. This
analysis is carried out for the quantum Ising chain as a transverse magnetic
field is changed. We consider the ground-state entanglement between a large
block of spins and the rest of the chain. Entanglement loss is seen to follow
from a rigid reordering, satisfying the majorization relation, of the
eigenvalues of the reduced density matrix for the spin block. More generally,
our results indicate that it may be possible to prove the irreversibility along
RG trajectories from the properties of the vacuum only, without need to study
the whole hamiltonian.
