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This paper continues the analysis of the quantum states determined by theuniversal asymptotic structure of four-dimensional asymptotically flat vacuumspacetimes 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 statelambda at infinity scri of M. It is done by means of the correspondence betweenobservables in the bulk and those on the boundary at null infinity discussed inprevious papers. The induction is possible when some requirements arefulfilled, in particular the spacetime M and the associated unphysical one areglobally hyperbolic and M admits future time infinity i^+. lambda_M coincideswith Minkowski vacuum if M is Minkowski spacetime. It is now proved that, inthe general case of a curved spacetime M, the state lambda_M enjoys thefollowing further properties. (1) lambda_M is invariant under the group ofisometries of the bulk spacetime M. (2) lambda_M fulfills a naturalenergy-positivity condition with respect to every notion of Killing time (ifany) in the bulk spacetime M: If M admits a complete time-like Killing vector,the associated one-parameter group of isometries is represented by astrongly-continuous unitary group in the GNS representation of lambda_M. Theunitary group has positive self-adjoint generator without zero modes in theone-particle space. (3) lambda_M is (globally) Hadamard in M and thus lambda_Mcan be used as starting point for perturbative renormalization procedure of QFTof phi in M

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property