Given a superposition of states "B" which is a subset of the suoerposition "A" of all possible states of a set of qbits, is there a quantum operation that produces superposition $R= B^C$, the complementary subset of "A", and in the process necessarily destroys "B", to avoid violating the no cloning theorem? If not, is there an operation that can produce an approximate complement ${B^C}(Approx)$?
Edit 1: @tsgeorgios has demonstrated in a comment that the proposed operation is not unitary in the general case, so wouldn't be possible in general. However, this challenge may be analogous to the challenge of cloning a superposition, which can't be done in general, but can be closely approximated if the set A of states are linearly independent. That means if there are N qbits, there can only be N states in the superposition A. Though cumbersome, any method for approximating the complement of information encoded in B would be potentially useful.