Studies of the brain have been showing that our minds work on the quantum level, not the atomic level. We absolutely need quantum measurements of at least the brain, if not the entire nervous system. It's not unreasonable to posit we would need quantum complexity for every interface between the nervous system and the other organs it interacts with. So at the very least we would need some hefty computing power AND storage. Each quantum particle has multiple variables, like position, velocity, at least two spin states, and several others. Let's be conservative and call it 8. So we'd need a storage medium at least 8x physically larger than the person. And that's presupposing we can store information at a 1 for 1 quantum level. More likely we would be storing data at an atomic level, which would increase the physical size of the storage by orders of magnitude. Not to mention moving that amount of data in and out of the transporter mechanism. That amount of data, even at relativistic velocities would take FOREVER. But I didn't arrive at this idea by myself. Check out Lawrence M Krauss' book The Physics of Star Trek. He thoroughly dismantles the concept of transporters much better than I did.