  Do correctness and completeness of quantum mechanics jointly imply that
quantum state vectors are necessarily in one-to-one correspondence with
elements of the physical reality? In terms of category theory, such a
correspondence would stand for an isomorphism, so the problem of the status of
the quantum state vector could be turned into the question of whether state
vectors are necessarily isomorphic to elements of the reality. As it is argued
in the present paper, in order to tackle this question, one needs to complement
the category-theoretic approach to quantum mechanics with the
computational-complexity-theoretic considerations. Based on such
considerations, it is demonstrated in the paper that the hypothesis of the
isomorphism existing between state vectors and elements of the reality is
expected to be unsuitable for a generic quantum system.
