Everybody™ thinks that quantum teleportation is lame. Even science-loving xkcd thinks quantum teleportation is lame, and has a comic mocking it:
This breaks my heart. I want to actually defend quantum teleportation, and show that Randall Munroe is wrong. Quantum teleportation is not a “particle statistics thing”.1 It is not worse than classical teleportation. Quantum teleportation is cool.
Let us start with something that everyone agrees is cool: Start Trek teleportation2. Some Scottish engineer presses a button, you dematerialize in the spaceship, and instantly rematerialize on the surface of an unexplored planet. This is completely impossible, so we have to get rid of non-essential elements to make it possible.
First of all, the “instant” part of the rematerialization. Einstein doesn’t like it, so we replace it with a suitable light-speed delay. After all, I don’t really care if I get to Mars instantly, or after a 20 minutes delay. It is still much better than getting on a rocket and playing Breath of the Wild for months while being bombarded with space radiation. Second and last, the “unexplored planet” part. How the hell are you supposed to rematerialize yourself alone on an unexplored planet? You’ve been dematerialized, probably into photons3, there isn’t much you can do. Is the spaceship supposed to do the rebuilding? How? Remotely moving stuff around with atom precision? Like some kind of long-range optical tweezers? Much easier to just build a rematerialization station on Mars. Yes, this stops you from teleporting to places “Where no man has gone before”4, but let’s be honest, do you really want to teleport somewhere without first making sure that the locals don’t find you tasty?
So with these changes, a realistic version of Star Trek teleportation becomes: Some Scottish engineer presses a button, you dematerialize in the spaceship, and after a suitable light-speed delay rematerialize on the surface of an already-explored planet. Easy, right? Sounds like just a glorified 3D printer. The Scottish engineer measures you with exquisitely high precision, sends the data via email, and the 3D printer makes a copy at the destination. And the Scottish engineer shoots you.
Wait what? Why is the Scottish engineer shooting you? And with what right the 3D-printed copy is claiming to be you in Mars? And what if the Scottish engineer does not shoot you, and the 3D-printed copy grabs a rocket back to Earth while you’re still stuck in the spaceship? What if your spouse wants to have sex with the copy? Who gets custody of the kids? What if you want to have sex with your copy? These vexing questions are often asked, but seldom answered.
An unexpected easy-way-out appeared in 1982, when Wootters and Żurek proved the no-cloning theorem. This theorem does what it says on the tin: it shows that it is not possible to clone a quantum state. Problem is, we don’t know if the whole quantum state of a human being is needed to define their interesting properties, or some classical approximation is good enough. But there are people seriously speculating that the whole quantum state is in fact needed, so we’ll assume that this is the case so that we can go on with the story.5
What happens in this case? Well now human beings are unclonable, unique. You can still be Star Trek-teleported to Mars, but now instead of being measured and shot by the Scottish engineer, they transfer your quantum state to a bunch of photons using something called a SWAP gate, reducing your body to a shapeless heap of atoms in the process. The photons fly away to the rematerialization station, where a second SWAP gate transfers the quantum state to suitably prepared shapeless heap of atoms, which then becomes you. The crucial difference is that your original body is destroyed not because you are uncomfortable with the idea of having a copy, or because the Scottish engineer hates you, but because it is fundamentally impossible to do the teleportation otherwise. The process is more akin to moving than to copying, and captures the original Star Trek intuition of transporting people without any unwholesome killing business.
But this is not yet quantum teleportation! But why should we bother with it, what is missing? Well, the problem is that quantum states are rather fragile. Send your quantum state through the Martian atmosphere, and you’ll see what happens. Well, no, you won’t see, because you’ll be dead. Your quantum state will most likely decohere away, and at the rematerialization station only a classical approximation will arrive which, as we assumed above, is not really you.
One can try to encode the quantum state in a way that it is resistant against atmospheric turbulence (and people are working on it), but quantum teleportation offers a more elegant solution: we just need to supply some entangled pairs of particles to the dematerialization and rematerialization stations, and you can be teleported via email, just like before! Good old email, that can be copied, stored, and resent as often as we can. But with the added bonus that once you are dematerialized, you can only be rematerialized once, and this can only happen at the rematerialization station in Mars.
The catch, of course, is how you supply the entangled pairs to start with. Nature allows no cheating: it costs exactly one entangled pair to teleport an entangled pair. Well, one can just try sending them through the atmosphere. Since they don’t encode any information, it is not a problem if we lose half of them. If the atmosphere is so bad that almost none of them gets through, them one can just do it the hard way: save them in a quantum memory, and send them via rocket.
So, is quantum teleportation cool?
Quantum teleportation is cool because it saves your soul