Quantum teleportation

Welcome to PhysicsForums, Yash!

The ability to teleport quantum states is extremely constrained. Even with photons, the teleportation is not of an eigenstate but rather a more general state - an entangled state.

So the answers to your questions are: no and no.

 

It's really unclear what you're trying to say here. For one thing, "an eigenstate" without further details doesn't mean anything. An eigenstate of what? Any pure quantum state is the eigenstate of some Hermitian operator. Second, quantum teleportation uses entangled states, but the state you teleport can be whatever you want.

 

Sorry, I don't get what you are trying to say. I don't think you disagree with my answer to the OP.

The only thing that can be teleported is the entangled state. You cannot teleport position, you cannot teleport momentum, you can't even teleport a spin of a specific known value. As far as I know, a superposition is all that can be teleported. Since teleportation occurs FTL if you so choose, anything else would effectively violate signal locality.

 

Are you confusing teleportation with entanglement swapping (a particular application of teleportation)? In basic teleportation, you have three states from the same Hilbert space—one arbitrary state to be teleported and two in an entangled pair. The one to be teleported can be anything you like . The entangled state is not what's being teleported, it's what you use to teleport the target state.

Huh? You certainly can teleport a specific known value of spin. If Alice wants to teleport a spin-up state to Bob, they prepare a Bell state and each take half, Alice does a unitary on her end with her half of the pair and the spin-up state and then does a Bell measurement, tells Bob the result, he does a unitary, and then he's got the spin-up state. Of course teleporting known states kind of defeats the point because Alice could just instruct Bob to prepare a spin-up state himself. The main point is that Alice can send any state to Bob, whether she knows what it is or not, at the expense of destroying her copy. This requires one Bell pair and two bits of classical communication as resources per qubit of quantum information teleported. I don't know if anything is known about teleportation with continuous bases, so I can't comment on whether it can be done with position and momentum. But I don't see anything fundamentally preventing it at least.

No, it does not, because quantum teleportation requires a classical communication channel to complete the exchange. It sounds to me like you need to review how quantum teleportation works.

 

Well I mostly agree with the above,but again don't see the relevance to the OP's question (which was what I was addressing). Teleportation is highly constrained (to what can be measured simultaneously) and requires classical information to make anything of what you teleported. You do NOT teleport a specific known state, you teleport one of several possible states; I guess you are correct to call it teleportation once the classical signals arrive and you put it all together. Of course position *and* momentum cannot be teleported, I am sure you mean position OR momentum.

A system of more than one particle (such a nucleus) would be far more complex to analyze and constraints on knowledge would prevent you from getting very close to describing it as it sits, certainly far less than you could describe a single photon. Think of the permutations of a helium nucleus.

So to answer the OP's question: there are limits on our knowledge of a nucleus as with any quantum object. There are severe constraints on how much of a quantum particle can be teleported at a time (as best as I know a single property at a time but perhaps someone else knows more on this point). Accordingly, there is no meaningful way to teleport a nucleus.

 

Well, OP was asking about quantum teleportation and your response had nothing to do with teleportation. So correcting it was very relevant.

Teleportation, by definition, is not completed until the classical information has arrived and been implemented. You seem to be assuming the original poster was asking about instantaneous teleportation of states. I see no such assumption in the original post. Quantum teleportation is not about doing something here and instantaneously having something happen there. Classical communication to complete the exchange, whether it's photons or OP's question about whole atoms, is assumed. That's not what I call teleportation it's what everyone in quantum information calls it. You do teleport a particular state, not a mixture, because the teleportation is not complete until Bob learns the results of Alice's measurement and modifies accordingly. You are using very standard terminology incorrectly.

Again, huh? States are teleported, not particular observables associated with states, so this comment doesn't even parse. One doesn't teleport "position" and "momentum". You teleport states that have some particular position and momentum representations (though, again, I'm not sure if teleportation has been shown to work in infinite dimensional Hilbert spaces—that is what I meant when I said I don't know if this works for position and momentum). Complementary observables, which it sounds like you're connecting this to, have nothing to do with this.

Once again, the entire point of teleportation is that you don't have the analyze the state you're trying to send. It is a method to allow you to move a state from A to B, without physically carrying it there and without having to know what state it is!

This is extremely frustrating. It's really clear you don't know what teleportation is about, but you're continuing to insist you've understood and answered OP's question. I think someone with the "Science Advisor" tag has the responsibility of not trying to speak authoritatively on topics they are unfamiliar with. There's nothing wrong with being unfamiliar with something, but just kind of making it up as you go is not acceptable. There are plenty of good resources to explain how quantum teleportation works and I think you should read some before contributing any more to this thread.


Yash, If the goal is just to have Alice teleport, say, a helium nucleus in a particular state to Bob and Bob has a helium nucleus onto which the state can be teleported, then I think the answer is probably yes. I think that might not be your question, though. It sounds like you're wondering whether or not the same techniques that let you move, say, a particular polarization state from one photon to another could be used to transport whole particles. In other words, what if Bob doesn't even have a helium nucleus, he just has some raw material that he make interact relativistically. Can Alice and Bob do something like teleportation with atom smashers of a sort such that if Alice wants to send Bob an electron or proton or a helium nucleus, then at the end of their protocol an electron or a proton or a helium nucleus pops out of Bob's machine. It's a very interesting question and I don't think anyone has the definite answer right now but I suspect it's probably no (though for very different reasons than DrChinese has been saying).

I think the biggest challenge, even if the techniques of quantum teleportation generalize sufficiently, is control over the states. If you're sending a spin-1/2 state, you need to be apply an arbitrary set of unitary operators to it and the entangled pair. Fortunately, applying arbitrary unitary operations to it is feasible (though not easy, ask the quantum computing people!). In particle physics, we don't have the same sort of Hamiltonian control. So, we generally can't, say, take a couple protons, smash them together very carefully, and get exactly the particles we want out at the end, we get a distribution of particles. Whereas with non-relativistic quantum mechanics, we can often tune the time evolution of the system how we like, in relativistic quantum mechanics (the regime where massive particles can be created) we're generally stuck with what nature gave us.

 

"How rude!"

-Jar Jar Binks :-) :-) :-)

Everyone's a critic. I'll stand by my answer to the OP, and you are welcome to yours.

 

If my terminology is bothersome, fine, I stand suitably corrected.

But you cannot perform quantum teleportation except in an extremely constrained manner. You need to place the two particles into a Bell state in the spin basis. To go any further, you would need to place them into an additional Bell state on some other, commuting basis. I am not knowledgeable enough to know how that could be accomplished, and have never even seen a proposal on how that might occur. So if anyone has a reference on that either way, I would be delighted to see it.

 

I think you can teleport a definite state, one of the first experiments that demonstrated teleportation did this. However I am currently on my tablet at work, so will need to look for the experiments article when I get home.

 

Found the article on the web. It is called 'experimental quantum teleportation'. Co authors include Anton Z. and Dik B. It is available on UCSB website - do a google search. I dont know how to copy and paste on this tablet.

EDIT: At home now - here is the article: http://web.physics.ucsb.edu/~quopt/exp.pdf

EDIT2: When I had email correspondence with William Wootters, I asked the following:
Is it possible to teleport a definite state photon - say a horizontally polarized photon - onto another photon (which I believe has to be in no definite polarization state)?
He replied 'yes'.