I assume by "consciousness" you mean self-awareness. A similar paradox is viewed within the context of quantum replication, i.e. an aboslute precise material co

I assume by "consciousness" you mean self-awareness. A similar paradox is viewed within the context of quantum replication, i.e. an aboslute precise material copy of your body is created, maybe even more than one, so the question is, what happens to your "I", your self-awareness in that case. One approach is to say "it doesn't matter" because self-awareness is illusory. It doesn't exist in the same sense as matter or fields. What does exist in your mind is memory of all state transitions ever happened in your brain. It's like a linked list going back, where each element is a state of the brain. That chain is mistaken for something that exists, whereas it's just a logically linked list of some data. You are nothing but information.