Now, consider this: if you step into the transporter room in Star Trek, and Scotty beams you planetside, essentially, he has vaporized you on the ship, and reconstructed you on the planet, with every atom and molecule arranged perfectly, thus your brain is exactly as it was in the transporter room, complete with your current thoughts and memories. You think you're the same guy. What the heck, it always seems to work, so why complain?
One day Scotty beams you down, and just like every other time, you arrive on the planet, memories intact, and go about your business. All is good. However, up on the ship, the transporter failed to vaporize you. One of Scotty's assistants walks up to you, and says "Sir, there's been a slight malfunction, but no worries, you're down on the planet. Now, if you'll just come with me...", as he leads you off towards the secondary vaporizer.
The point, of course, is what does it mean to have your consciousness live on?
1) Thats not real so any question leading up to it is irrelavent
2) Lets get to the transporting stage first to prove the theory once and for all. Pay someone alot of money and it will happen.
There's no need to for transporters to be real to follow the logic of the thought experiment. The scientists who worked out quantum theory did nothing but thought experiments themselves.
You're doing yourself a disservice by making the ridiculous assumption that a transporter be real to draw conclusions from the thought experiment.