" wrote:

Can it not be used to copy the position of an atom ?

For example, if I have 3 entangled photons, can I copy the position of
an atom to 3 bits of resolution ?

Step one: confirm the source atom is in a volume much larger than
Heisenberg's limit.

Step two: Do some fancy measurements in conjunction with the photons.
The measurements would be a binary search or something.

Step three: Use the other half of the photons + results of measurement
to position the other atom.

This then copies the atom's position ... but only to 3 bits of accuracy.

I can't tell what you're asking. Your words do not match anything I
know of regarding quantum teleportation.

What quantum teleportation does is to transfer the quantum state of a
target object to to a destination object with perfect fidelity. That
would be something like its polarization or its spin. It has to lose
the original state in the process, so it isn't able to "copy" anything.

(Position can already be measured to an arbitrary precision using
classical methods, though you lose information on momentum as you gain
it in position and vice versa.)