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For anyone in this community that's familiar with quantum teleportation, I need desperate help. I am currently working on my senior thesis and my goal is to teleport a molecule.

Background: So in quantum teleportation, you are only teleporting the information. This has been done with spin states of atoms, polarization states of light, atoms (ions actually). In the teleportation of atoms, they are teleporting the internal quantum state... the eigen states that correspond to the eigen energies which are the quantum states and their corresponding energy levels. However, I'm not so concerned with teleporting the internal states because I'm thinking that all that matters is the position and momenta information and not the internal quantum states. But I"m a little confused and unsure here in that statement.

There exist such a thing as "translational entanglement" where two atoms are translationally entangled, which means that the position measurement of one particle is correlated with the momentum measurement of the second particle. It is the original EPR state that was proposed by (Einstein–Podolsky–Rosen. There are papers that have described ways of using this type of entanglement to teleport the translational state of atoms.

So how it breifly works is as follows. You start out with a molecule, say H2, and you can use use laser to dissociate it such that the two atoms remain translationally entangled, saying it another way, they are still considered one system. The translational entanglement dimishes as time increases and as they separate farther apart. You can preserve this entanglement by applying a double well harmonic oscillator that parametrically expands with the two particles.

Important to know here, when you establish your quantum "link" or "channel" they have to be of the same type of atoms and the same type with what you want to teleport.

So once you've established this, you are ready to interact another system, the thing you want to teleport, with one of the entangled pair of atoms. This interaction is measured in a sophisticated way, and dependent upon the position and momenta measurement of the combined system, you can manipulate the other entangled pair to assume the same position and momentum with respect to its coordinates.

Here is the paper the describes what I'm saying in more detail. http://iopscience.iop.org/0295-5075/75/6/847;jsessionid=3A199A26FE1675A13BADDDFB54B185DA.c1

My question/problem I desperately need help in

So I'm trying to do something like this but with a molecule. So I want to have the input state to be a molecule. So I need two quantum channels, each that corresponds to the two atoms that make up the molecule I want to teleport. I'm doing this theoretically.

So we have particle a1 entangled with particle b1 and particle a2 entangled with b2. Now particle a1 and a2 are in laboratory A and particle b1 and b2 are in laboratory B. The input molecule is H2, molecular hydrogen. The particles a1, a2, b1, and b2 are hydrogen atoms. Now I want a interact the molecule with particles a1 and a2, and measure the joint system's position and momenta. Now with this information, I want to manipulate particles b1 and b2 so that they assume the input state's position and momenta, THUS BECOMING A MOLECULE!

My question is, "Is all that matters is the translational information about molecules, or does the internal states of the atoms matter too?"

Because I want to be able to say that this can be expanded to more complex molecules like water. We can have three quantum channels, two that are hydrogen atoms and one that is oxygen atoms. Doing it more complex, we can do the same thing for a DNA molecule. (Going a bit far here.)

Quantum teleportation via translational entanglement seems to be the way of ACTUALLY teleporting material objects, because you get the molecule on the other side. What most physicists are focusing on is when you have the same atom in laboratory A and B. So its pointless if I want to teleport an atom, cause you already have it on the other side! What they are concerned with is teleporting the quantum state for quantum computing. If you are familiar with quantum teleportation, you know what I mean. "I'm thinking that the quantum state of a molecule, its position and momenta of all the atoms, can be teleported and mapped onto atoms in laboratory B to get them to turn into the molecule." That's what I'm trying to do here.

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