This fun, amusing, and back-of-the-envelope calculations done by a group of students at the University of Leicester in England shows that to sample and transport all the information about a human to another location (as in the Star Trek teleportation device) will just take too long for it to feasible right now.
Our universe has been around for 13.8 billion years. But the seriously tongue-in-cheek paper shows that at a beaming speed of 30 gigahertz, transmitting all the data within a single human would take 4,850,000,000,000,000 (4.85 quadrillion) years. The human dataset includes not only the person's genetic code but also all the memories and knowledge stored in his/her brain. While DNA would take up about 10 billion bits, the brain's information would bring the data total up to 2.6 x 1042 (26 followed by 41 zeroes) in bits.
Why not simply increase the bandwidth to speed up the process? That would require an impossible increase in power consumption beyond earth's capabilities.
I think there's something else here that should be pointed out, and something that many non-scientists should be aware of. When we think "outside of the box", we must (i) first know where the box is and where its boundary is (which means one must have the established knowledge first), and (ii) be able to make quick, back-of-the-envelope estimation to tell us if the quantitative aspect of what we wish to do or study produce a reasonable, achievable goal.
The latter is quite important, because it tells us if there's any reasonable chance that we can verify, or accomplish our goal. This means that a device, a detector, an instrument, etc. of certain parameter can either produce, detect, or accomplish that goal. When we seek support to do such work, we must show this because, as is very obvious, no one is going to fund something based on some handwaving argument, and they are especially not going to fund something if the numbers tell us that there's no REASONABLE chance for success!
So if someone wants funding to build such a teleportation device above, would you fund it knowing that it will take 4.85 quadrillion years to transport a human being? If you would, I have a bridge to sell to you.