The main problem here is with the use of the term "teleportation", which is typical overhype. What can be achieved with quantum entanglement is not what from science fiction you in any sense or under any circumstances would understand as teleportation.
Here is an easy way to understand quantum entanglement.
Lets say I give you two identical boxes. In one you put a red ball and in the other you put a blue ball. Then you mix them up and I take one of them to the moon. You have no idea what colour ball is in my box or your box.
You now open your box and it has a blue ball in it. You instantly know that I have a red ball in my box. Relativity is not violated here because I still have no idea what colour is in my box until either I open it or you tell me what was in you box - and you cannot get that information to me faster than the speed of light.
The reason for this very obvious instantaneous transfer of information is that the rules of the system - our two boxes - allowed their states to be entangled with one another. In other words, if one box contained a blue ball the other must contain a red ball - no other reality was possible.
Now it happens in quantum mechanics that this is exactly how some systems behave. For instance, take two electons in a single box (so a single system) and cool them to the lowest possible energy - this is called the ground state. The rules electrons (which are fermions) obey say that no two can be in the same state, and when they both have the lowest possible energy the only difference between two of them can be that one has its spin up and the other spin down (spin is just a rather misnamed property of electrons - don't worry about what actually causes it). If they both had the same spin, one would have to have higher energy.
Now we have prepared our box with these two electrons their quantum states are entangled. However far we separate them - in other words however long we make the box - one is in one state and the other is in the opposite state, but we have no idea which is which.
Imagine measuring the spin of one electron at one end of the box. You instantly know the spin of the other one.
This information transfer is what is being referred to as teleportation. It is possible to construct entangled systems that replicate the state of electons or other particles remotely.
You are not really moving an electron from A to B - you are just using the fact that all fundamental particles are indistinguishable (they do not have labels saying this is electron Fred, and this is electron Jim). All that can be said about them is their state.
This is a far cry from transporting the information about a complex system like even a single atom.