Maybe you've just used "items" in a non-standard way? The number of bits (N) is indeed being halved, but the standard way of talking about Grover's search is t

Maybe you've just used "items" in a non-standard way? The number of bits (N) is indeed being halved, but the standard way of talking about Grover's search is that you're searching for an item in the "database" of bit configurations (i.e., keyspace), which is 2^N. No one would refer to the bits as "items".