Mathematical Breakthrough Sets Out Rules For More Effective Teleportation

dsinc sends this news from the University of Cambridge: "For the last ten years, theoretical physicists have shown that the intense connections generated between particles as established in the quantum law of ‘entanglement’ may hold the key to eventual teleportation of information. Now, for the first time, researchers have worked out how entanglement could be 'recycled' to increase the efficiency of these connections. Published in the journal Physical Review Letters, the result could conceivably take us a step closer to sci-fi style teleportation in the future, although this research is purely theoretical in nature. ... Previous teleportation protocols have fallen into one of two camps, those that could only send scrambled information requiring correction by the receiver or, more recently, "port-based" teleportation that doesn't require a correction, but needs an impractical amount of entanglement – as each object sent would destroy the entangled state. Now, physicists from Cambridge, University College London, and the University of Gdansk have developed a protocol to provide an optimal solution in which the entangled state is 'recycled,' so that the gateway between particles holds for the teleportation of multiple objects. They have even devised a protocol in which multiple qubits can be teleported simultaneously, although the entangled state degrades proportionally to the amount of qubits sent in both cases."

Re:Where does extra energy go?

[Anonymous Coward]

The name "quantum teleportation [wikipedia.org]" is a bit misleading: no particles, mass or energy is teleported. The only thing "teleported" is a quantum state.

What's remarkable about quantum teleportation is that you can transfer an exact quantum state from one place to another without sending any particle with that state along the way. That's remarkable because quantum states can't, in general, be copied (see the "no-cloning theorem [wikipedia.org]). When you perform a quantum teleportation, you must destroy the state of the originating particle during the teleportation process.

Re:Where does extra energy go?

[Neil Jacklin]

Actually, the object does have _potential_ energy. I've wondered about OP's question before. I think the answer has to do with the fact that these "teleporters" don't transport matter in the conventional sense. Suppose you did have have a teleporter that could take an object and teleport it 100 ft up a hill. If you dropped the object, collected the potential energy (like in a waterwheel), and teleported it again, you shouldn't be able to violate conservation of energy or make a perpetual motion machine. So, I figure it's either A) impossible, or B) requires an energy input at _least_ equal to the change in potential energy. \\ Of course, I'm talking about gravitation potential energy, but that's just one field. There's also electromagnetic. Conversely, if it took more energy in than the net change in potential energy, where would that energy go? So I suppose the net energy input should be equal to the change in potential energy. \\ This also raises other issues, like if I teleport very far away, or two a more massive planet, I might need to input a lot of energy on this side. \\ A possible resolution to this problem is that the kind of teleportation here is just informational--that is changing one particle's state to match (or oppose) the one on the other side. Thus no mass (or charge) is transported anywhere, and everything is happy energy-wise.

Re:Where does extra energy go?

[martin-boundary]

Potential energy "exists" inside the gravitational field: It represents the total amount of work you have to do to traverse a certain path while being subjected to the effects of the field. For a conservative field like the gravitational one, the amount of work is independent of the actual path when the end points are fixed, and that's the reason, the only reason, why we can associate a single number, called potential energy, with any given height above ground level.

In other words, potential energy is a mathematical shortcut, it saves you from having to compute a work path integral for each problem involving a particle traversing some path in a conservative field. Potential energy is literally a table of precomputed answers. If you have a path from 1000 feet down to 0 feet, you can 1) compute the work over that path or 2) look up the answer from the potential energy table, by subtracting the values at 1000 and 0 respectively. This works because of the fundamental theorem of calculus.

Now onto the question. If you teleport an object from 1000 feet to 0 feet, there is no traversal of the gravitational field by definition. Therefore there is no work being done against the field since there is no continuous path. Therefore there is no energy change experienced by the object since there is no physical work happening that involves it (disregarding whatever mechanism enables the teleportation in the first place).

Thus: At 1000 feet, the object has zero kinetic energy, and has potential energy V(1000). At 0 feet, the object has zero kinetic energy, and has potential energy V(0).

This does violate the conservation of (kinetic + potential energy), however that quantity is only a convenient approximation of the truth for non-teleportation cases, where the only way of arriving at 0 from 1000 feet is by traversing a continuous path. The truth is that (kinetic + work-over-path) is conserved, in this case, since the path is not continuous.