No, Chronos, it definitely does not work the way you think. In fact, Tim314 is even a little understimating the problems, because the entire waveform’s odds occur all at once, so it’s an all-or-nothing approach for multiparticle waveforms. For something as large as even a small visible object, the number of particles and the mathematical requirements are unimaginably absurd. Plus, we don’t even know of any way to even start entanglement on multiparticle waveforms.
It’s true that the dimension of a large quantum system is huge (2[sup]N[/sup] for a system of N two-state particles, as tim314 says above). Nevertheless, Chronos is right about the number of measurements required and the amount of data which must be transmitted. Quantum teleportation preserves the quantum state of a particle, including its entanglement, so you don’t have to measure the whole system at once. You can, at least in principle, measure and teleport the system one qubit at a time, requiring only two bits of communication per qubit teleported.
No, I don’t think it can actually work like that, becaue you can’t simply seperate particles from the total waveform. It has to be measured and tramsmitted all at once, or it just won’t, because the “teleportation” is inherently random.
You are correct that you can’t do a coherent quantum teleportation by individually measuring each particle and transmitting its state; the reason, as you state earlier, is that the state of the quantum system is almost entirely hidden in the entanglements between particles, which cannot be seen in single-particle measurements; and this state is also incredibly large for a macroscopic system, far too big to represent practically with a string of bits.
However, quantum teleportation does not work like that. In quantum teleportation, you perform a particular two-qubit measurement, on the qubit you wish to teleport and one qubit of an entangled pair. This measurement is guaranteed to give a random outcome, providing no information at all about the state of the system you wish to teleport. When you transmit this information to the other qubit of the entangled pair and a particular operation is done on that qubit, the state of the original qubit is reproduced exactly on the other end of the teleport, including all entanglements the qubit may have originally had. If you teleport a many-qubit entangled state one qubit at a time, you end up with the same entangled state at the other end, even though the measurements tell you absolutely nothing about the state you just teleported.
In practice, there are obviously problems with this (the teleported qubit no longer is strongly interacting with the particles that used to be its neighbors, etc.), and maybe that’s what you’re getting at. But in theory you can indeed teleport an arbitrary quantum system one qubit at a time.
Omphaloskeptic, I think you’re right that the sender’s two-qubit measurements transfer the entanglement of her qubits to the receiver’s qubits. But the qubits of the receiver (“Bob”, conventionally) won’t end up in the same entangled state that the qubits of the sender (“Alice”) started in. In the one-qubit case, Bob has to perform a local operation on his qubit based on the results of Alice’s measurement in order to make his qubit have the state that hers started with. I would think that in the N-qubit case Bob would have to perform an N-qubit operation on all of his qubits after receiving the results of all N of Alice’s two-qubit measurements. Performing an N-qubit operation is hard enough, but since each of Alice’s measurements had four possible outcomes that means there are 4[sup]N[/sup] possibilities for what Bob’s N-qubit operation will need to be – which for macroscopic systems is more than he can possibly keep track of.
Are you saying I’m wrong, and Bob can actually correct his state just by performing N one-qubit operations? It could very well be that I am wrong – I’m much more familiar with the one-qubit teleportation protocol. (Like I said, my advisor is an expert on this stuff, but I’m not – my doctoral work was in a different area of his research.) I suppose if I really wanted I could work it out on paper for the two-qubit case, but I haven’t bothered to do this.
It strikes me that another problem with teleporting macroscopic objects is that the states available to your atoms may change depending how close they are to other atoms (for instance, whether they’re involved in molecules). I’m not sure how quantum teleportation would deal with this. For some situations, it wouldn’t matter – I mean, if you’re building a quantum computer you could have a bunch of non-interacting atoms as your memory (say, atoms in a deep optical lattice), and talk about teleporting the state of your computer’s memory into another computer’s memory. But for an ordinary macroscopic object the atoms form complex molecules and thus inevitably are interacting with each other.
Alice does a measurement and communicates the 2-bit result to Bob, who performs one of four unitary operation depending on the bits he got from Alice. The result is that Bob’s qubit is now in exactly the same quantum state as the one Alice teleported, entanglements and all. From a formal Hilbert-space viewpoint, the state of the N-qubit quantum system is exactly the same as it was before; all that’s been done is a relabeling of the qubits. This is true independent of where the other N-1 qubits are (since nobody had to look at the other N-1 qubits at all), so it’s as true for the second, or nth, qubit they teleport as for the first.
Yes, this is what I was alluding to in the last paragraph of my post. The state at the time of teleportation is unchanged, but the teleportation may radically change the system evolution if the teleported particle was interacting strongly with other particles in the system. Teleporting arbitrary macroscopic systems is obviously much harder than teleporting systems where you can control the interparticle interactions.
Having looked at it a bit more, I see you’re quite right Omphaloskeptic. After Alice perfoms her measurement, Bob’s qubit can only differ from the desired result by a local operation. So there’s no need for him to perform many-qubit operations, as I’d feared.
Even so, I doubt we’ll ever see quantum teleportation of arbitrary macroscopic objects – certainly not within our lifetimes. Aside from the aforementioned issue of the interactions between the atoms, there’s the fact I alluded to above, that performing some 10[sup]23[/sup] measurements, transmitting the results of each, and then performing the appropriate local operation for each one is going to take a long time. Even teleporting one qubit per femtosecond this would take years, and good luck getting your macroscopic object (particularly its entanglements) to hold still for that long.
It’s also worth noting that in your macroscopic object each atom won’t simply correspond to a single qubit, since they’ll have many more than two possible states. Not that this prohibits teleportation, but it’s one more complication to deal with.
I imagine many-qubit teleportation will be much more likely to become practical and useful for things like moving around information in quantum computers. There you really could have noninteracting atoms (or ions or whatever) with each particle corresponding to a qubit, and even for large computations you wouldn’t need anywhere near macroscopic numbers of qubits.
Who in the world has left over atom smashers stored in the garage?
Now I don’t know whether to ask in this thread or the God Particle thread, but anyway: if the Higgs particle is what gives fundamental particles their mass, and can thus be described by quantum field theory, does that mean that quantum teleportation could include an object’s mass as part of it’s quantum state? And would that mean that mass can be teleported?
We actually don’t even need to know anything about the Higgs to answer this. The mass of a particle is a measure of how much energy it has when it’s standing still. Thus if two states have different energies, they have different mass.
However, we cannot teleport mass. The short answer is that any change in the mass of the receiver’s particle has to be added by the receiver himself in order to complete the teleportation.
For example, say you have two states (call them 0 and 1) with different mass, and let’s say the particle we want to teleport is in state 1 (the state with more mass). In order to be able to teleport it, we start with the receiver’s particle in an entangled state with another one of the sender’s particles. In this entangled state there is some quantum mechanical uncertainty about the mass of the receiver’s particle. If we were to measure its mass, there would be a 50% chance of finding it in state 0 with the lesser mass, and a 50% chance of finding it in state 1 with the greater mass. (Note that we’re probably only talking about a very small difference in mass here – the greater the difference, the more rapidly the system will decay into the lower energy state by, say, spontaneously emitting a photon.)
To perform the teleportation, the sender first performs a measurement on their particles. Because of the entanglement, this also has the effect of measuring the state of the receiver’s particle. Half the time the receivers particle ends up in state 0 and half the time in state 1, just as we expected. If it ends up in state 1, the receiver doesn’t need to do anything. If it ends up in state 0, the receiver completes the teleportation by transfering it to state 1, in the process contributing the difference in energy himself.
The teleportation procedure also works to teleport a state of indefinite mass (e.g., a superposition of 0 and 1), but the general idea is the same.