Classical Teleportation Is Easier Than Quantum Teleportation

Quantum teleportation confuses people.

Maybe you’ve heard the buzzword, and you imagine science fiction become reality: teleporting people across the galaxy, or ansibles communicating faster than light. Maybe you’ve heard a bit more, and know that quantum teleportation can’t transfer information faster than light, that it hasn’t been used on something even as complicated as a molecule…and you’re still confused, because if so, why call it teleportation in the first place?

There’s a simple way to clear up this confusion. You just have to realize that classical teleportation is easy.

What do I mean by “classical teleportation”?

Let’s start with the simplest teleporter you could imagine. It scans you on one end, then vaporizes you, and sends your information to a teleportation pad on the other end. The other end uses that information to build a copy of your body from some appropriate raw materials, and there you are!

(If the machine doesn’t vaporize you, then you end up with an army of resurrected Derek Parfits.)

Doing this with a person is, of course, absurdly difficult, and well beyond the reach of current technology.

transporter2

And no, nothing about the Star Trek version changes that

Do it with a document, though, and you’ve essentially invented the fax machine.

Yes, faxes don’t copy a piece of paper atom by atom, but they don’t need to: they just send what’s written on it. This sort of “classical teleportation” is commonplace. Trade Pokémon, and your Pikachu gets “classical teleported” from one device to another. Send an email, and your laptop teleports it to someone else. The ability to “classically teleport” is essential for computers to function, the idea that you can take the “important information” about something and copy it somewhere else.

Note that under this definition, “classical teleportation” is not faster than light. You still need to send a signal, between a “scanner” and a “printer”, and that’s only as fast as your signal normally is. Note also that the “printer” needs some “ink”, you still need the right materials to build or record whatever is being teleported over.

So suppose you’re building a quantum computer, one that uses the unique properties of quantum mechanics. Naturally, you want to be able to take a quantum state and copy it somewhere else. You need “quantum teleportation”. And the first thing you realize is that it’s harder than it looks.

The problem comes when you try to “scan” your quantum state. You might have heard quantum states described as “inherently uncertain” or “inherently indeterminate”. For this post, a better way to think about them is “inherently unknown”. For any quantum state, there is something you can’t know about its behavior. You can’t know which slit the next electron will go through, you can’t know whether Schrödinger’s cat is alive or dead. If you did, the state wouldn’t be quantum: no matter how you figure it out, there isn’t a way to discover which slit the electron will go through without getting rid of the quantum diffraction pattern.

This means that if you try to just “classically teleport” a quantum state, you lose the very properties you care about. To “scan” your state, you have to figure out everything important about it. The only way to do that, for an arbitrary state on your teleportation pad, is to observe its behavior. If you do that, though, you’ll end up knowing too much: a state whose behavior you know is not a quantum state, and it won’t do what you want it to on the other end. You’ve tried to “clone” it, and there’s a theorem proving you can’t.

(Note that this description should make sense even if you believe in a “hidden variable” interpretation of quantum mechanics. Those hidden variables have to be “non-local”, they aren’t close enough for your “scanner” to measure them.)

Since you can’t “classically teleport” your quantum state, you have to do something more subtle. That’s where “quantum teleportation” comes in. Quantum teleportation uses “entanglement”, long-distance correlations between quantum states. With a set of two entangled states, you can sneak around the “scanning” part, manipulating the states on one end to compute instructions that let someone use the other entangled particle to rebuild the “teleported” state.

Those instructions still have to be transferred normally, once again quantum teleportation isn’t faster than light. You still need the right kind of quantum state at your target, your “printer” still needs ink. What you get, though, is a way to transport the “inherently unknown” behavior of a quantum state, without scanning it and destroying the “mystery”. Quantum teleportation isn’t easier than classical teleportation, it’s harder. What’s exciting is that it’s possible at all.

 


 

On an unrelated topic, KKLT have fired back at their critics, with an impressive salvo of papers. (See also this one from the same day.) I don’t have the time or expertise to write a good post about this at the moment, currently hoping someone else does!

5 thoughts on “Classical Teleportation Is Easier Than Quantum Teleportation

  1. Adam

    I don’t really like your “inherently unknown” : in most cases, the quantum state can be perfectly know (because you made it, or because you characterized it using quantum tomography). Much in the same manner, what is “inherently uncertain” or “inherently indeterminate” is not the state, but the measurement. It is not because you don’t know if the cat is dead or alive before the measurement that you cannot know the quantum state of the decaying atom exactly.

    And we can definitely classically teleport quantum states (using your definition of classical teleportation for emails) : I can characterize a quantum state (using tomography), send the measured density matrix by email, and if you have an apparatus that “print” quantum state (say a well controlled photon source), you can create a system in the same state.

    In fact, the arXiv (in particular the quantum physics section) is the biggest classical teleportation machine in the world, by your definition 😉

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    1. 4gravitonsandagradstudent Post author

      Yeah, in retrospect I think a big weakness of my post is that it equivocates between two senses in which you can “know” about a quantum state, and hence two senses of cloning one (“make a state using exactly the same procedure” versus “the thing prohibited by the no-cloning theorem”). It’s a crucial element in the no-cloning theorem that you don’t have access to the process that made the state, so you can’t do quantum tomography, it’s just some arbitrary state you have to work with. I didn’t really make that clear in the post, I should probably rework things so that has a clearer role in the explanation.

      I do think “inherently unknown” is a good way to convey the key element here, the “you can’t just put it in a scanner and know everything about it”. But “everything about it” indeed includes “what exactly it will do when you measure it”, and I should figure out how to make that clearer in the post.

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      1. Adam

        Fair enough, my comment definitely assume that one has access to large number of realizations of the quantum state.

        Although I agree that “inherently unknown” is fine for a unique quantum state (since indeed it allows to perform only one measurement), I think it is misleading when discussing quantum states in general : for the typical experience you mention (double slit and schrodinger’s cat), one has access to an arbitrary number of state, and the density matrix is definitely known. What is important in these case is that even if you know the state exactly there is an uncertainty in the results of the measurement. Or if you prefer, the result of a measurement is inherently unknown in advance 😉

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        1. 4gravitonsandagradstudent Post author

          For what it’s worth, part of the awkwardness of phrasing here is that I’m specifically trying to avoid using the word “measurement”. Because it’s a term with technical meaning, using it in a post like this risks readers confusing the everyday meaning with the technical one, which in practice seems to lead to a lot of additional confusion, including all sorts of weird mystical nonsense. So I’ve been trying to talk around it, and present things in a way that doesn’t lead to the same confusion. It looks like I haven’t quite succeeded though, I’ll have to think about how to rephrase things.

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