  We consider a spin chain extending from Alice to Bob with next neighbors
interactions, initially in its ground state. Assuming that Bob measures the
last spin of the chain, the energy of the spin chain has to increase, at least
on average, due to the measurement disturbance. Presumably, the energy is
provided by Bob's measurement apparatus. Assuming now that, simultaneously to
Bob's measurement, Alice measures the first spin, we show that either energy is
not conserved, - implausible - or the projection postulate doesn't apply, and
that there is signalling. An explicit measurement model shows that energy is
conserved (as expected), but that the spin chain energy increase is not
provided by the measurement apparatus(es), that the projection postulate is not
always valid - illustrating the Wigner-Araki-Yanase (WAY) theorem - and that
there is signalling, indeed. The signalling is due to the non-local interaction
Hamiltonian. This raises the question of a suitable quantum information
inspired model of such non-local Hamiltonians.
