In the film The Prestige, Hugh Jackman acquires a machine that creates exact duplicates of him, but they are all descrete, separate individuals with no more consciousness shared between them than between any other pair or group of people. Each is interchangeable to all outward appearances, but their respective consciousnesses are unique and limited to each separate duplicate.
The point is that even if they are all him, any one's consciousness is the only one relevant to that particular copy. Consciousness is an emergent phenomenon inextricable from its physical trappings. It cannot be handed off like a baton. If you are perfectly duplicated down to the quantum level, and that duplicate replaces you, the outside world may never know, but one of those two consciousnesses ceases to exist along with the matter in which it was rooted. Duplicating ones consciousness offers no more immortality than a flawless doppelganger taking your place. It can be "you" in every measurable way, but absolutely separate from the you that you are.