Remember that while it is very unlikely for all of your particles to quantum tunnel at the same time, it is even way more unlikely that they all quantum tunnel the same distance, so you really don't want to do this kind of teleportation as it is way more likely you'll completely disintegrate.
Measuring the 'quantum state' of a particle is not even possible. The quantum state is a superposition of all the possible measurable values times their probability. However, as soon as you measure, you force the quantum state to change to the measured value. Unfortunately, different measurable quantities can not have the same quantum state, i.e. you can nog measure impuls and position at the same time because there is no quantum state that represents just one measurable value of both impuls and position. So we'd have to measure multiple times and get an average but the state already changed the first time we measured so we can't do that(nor is there a phisical way to measure these values without exposing your body to an environment it can't handle)
Now is this a problem? No, I believe it is not. Is knowing the exact quantum state of your body really that relavent? While reading my post, you have changed a lot on a molecular level, the amount of molecules of each type has changed significantly and there position and kinetic energies aswell. Yet you don't feel you're completely different. What the original poster suggested might not be that bad, capture the state of your neurons and say that state is what makes you to who and what you are, your soul so to speak. Then transport this information and put it in a different body at the other end. That other body would then have the same nerve impulses as you had, weather or not it is still you is up to you to decide though.
This is not teleportation though as you are still only moving at the speed of light at most and not instantly
Infractions, reputation, reflection, the dark side of scripting, they are.