  This paper continues the analysis of the quantum states determined by the
universal asymptotic structure of four-dimensional asymptotically flat vacuum
spacetimes at null infinity M. It is now focused on the quantum state lambda_M,
of a massles conformally coupled scalar field phi propagating in M. lambda_M is
``holographically'' induced in the bulk by the universal BMS-invariant state
lambda at infinity scri of M. It is done by means of the correspondence between
observables in the bulk and those on the boundary at null infinity discussed in
previous papers. The induction is possible when some requirements are
fulfilled, in particular the spacetime M and the associated unphysical one are
globally hyperbolic and M admits future time infinity i^+. lambda_M coincides
with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in
the general case of a curved spacetime M, the state lambda_M enjoys the
following further properties. (1) lambda_M is invariant under the group of
isometries of the bulk spacetime M. (2) lambda_M fulfills a natural
energy-positivity condition with respect to every notion of Killing time (if
any) in the bulk spacetime M: If M admits a complete time-like Killing vector,
the associated one-parameter group of isometries is represented by a
strongly-continuous unitary group in the GNS representation of lambda_M. The
unitary group has positive self-adjoint generator without zero modes in the
one-particle space. (3) lambda_M is (globally) Hadamard in M and thus lambda_M
can be used as starting point for perturbative renormalization procedure of QFT
of phi in M.
