A skepticism on the concept of quantum state related to quantum field theory on curved spacetime

Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have the purely mathematical notion of states on a C^*-algebra mathfrak{A}, but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical "fictional" states. Only the states which can be expressed as a density matrix on a fixed "physical Hilbert space" the GNS representation space of $mathfrak{A}$ w.r.t. the vacuum are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call "pragmatic realism on quantum states", which insists as follows: "We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics." I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it.