Quantum Teleportation & Beyond!

Even before I studied Math & Physics in University, I had already read many popularized accounts of the 2 pillars of Physics, Quantum Physics & Einstein's General Relativity. I also read biographies of the geniuses like Erwin Schrodinger that contributed the most to these theories. But it wasn't till I studied the math behind Quantum Mechanics that I understood (about as well as anyone can!) where all those weird properties that exhibit themselves in the world of atoms come from.  This isn't what I'll be focusing on in this post but aside from the more technical links above, here's a great introductory link at a high level that covers the many strange properties that pop up in the micro-world!

Probably the most out there result (that's on solid theoretical & experimental footing) is what Einstein called "Spooky action at a distance", something called Quantum Entanglement (for a good high level summary, check Chris Craddock answer then Brian Dodson's).  This phenomena is essential to most of the other interesting aspects of QM such as below.

I've been reading quite a bit about new research in Quantum Teleportation, which at our current understanding has 3 parts in order of how well we have understood & tested

1. Quantum Teleportation of States (Paper appeared 1993 -- essentially transporting Quantum properties of 1 particle to another, arbitrarily far away with some caveats of course.  AFAIK the best anyone has done is teleport 2 quantum properties of a Photon.  So why is this Teleportation? Because most quantum particles are indistinguishable and hence if you can pass over their handful of quantum properties (from 1 particle to another) they are effectively cloned or transported if you will potentially half way across the galaxy!
2. Quantum Energy Teleportation (Paper appeared 2008 -- the simplest explanation I have seen is part of this thread on QET -- "The analogy Hotta uses is that the vacuum energy is in a safe. Alice unlocks it with a key and puts some energy in the safe. Weirdly, opening the safe tells her what the key is, rather than her having the key initially. She then sends her key to Bob, who is able to open the safe with it and get at the energy Alice put in!")
3. Quantum Teleportation of Particles with Mass (this last one is at the very edge of current research so it's all a bit tenuous but I believe QT of Electrons has not been achieved yet, though at least we are close due to this new research -- also 1 other reliable link I found on this but don't fully understand yet).

While each of the 3 topics above is very interesting in their own right, the possible applications are what's mind blowing.  

First, the most prosaic one is the application to quantum computers & communication, essentially building a Quantum Internet.  Last year, a Chinese consortium placed the first Quantum Satellite in orbit, this article sums all these topics nicely.  Essentially, the most obvious benefit of a Quantum Internet is security but new applications ideas are popping up all the time, such as the cool one at the end of the article.

My fave application comes from Star Trek, an actual Transporter that can transport people across vast distances.  However, this problem is still being debated from a theoretical point of view...from an Engineering point of view it's going to make creating AI or the 1st Quantum Computer look like child's play!  I personally believe it is theoretically possible (which means at some point - who knows when - it will be implemented).  This link from a CalTech PhD, working at Perimeter explains it very well in fairly simple terms (the link also explains #1 above very well too at the same time, he also explains how Physicist's fall into 3 groups on their views regarding the feasibility of...he too is in the same camp as me).

Before we get into some technical details/highlights from the math/physics...I highly recommend reading this wonderful philosophical account of "What Makes You You?", it's not a short read but it should blow your mind!  Also, one of the sections in the prior link is called "The Cell Replacement Test", many people believe somehow the particles that make us up have something (individually) to do with our identify/sense of self so it surprises them to know that most of our cells (particles) are replaced in 7-10 year cycles (crucially not neurons in the cerebral cortex so this alone isn't conclusive of anything just more evidence).  Finally some interesting insights that I mostly share can be found here (check Bill C. Reimers answer)...I especially like his simplistic but effective analogy of a conscious human being vs. a book, it's not the paper or the particles it's the Information contained that gives us and the book life.  Based on all the facts I've seen to date, I believe our consciousness is an emergent phenomena.

Some points on Teleportation I would add/highlight are:

• Some argue Teleportation (of people) is impossible due to Heisenberg's Uncertainty Principle, but this was shown to be not necessary in the groundbreaking 1993 Bennet et al paper I linked in #1.  For more explanation of this non-trivial point check here and here.
• Next common argument against is the Quantum "No Cloning Theorem" (a general Quantum State copying machine cannot exist) , this one took me some time to research (my initial argument against it was arbitrary approximation, which at the scale of humans may be needed but not at the particle scale), turns out that this theorem doesn't prevent Teleportion, in computer parlance it is NOT a Copy-And-Paste procedure but instead a Cut-And-Paste (c.f. Erik Anson's answer), so the original Quantum State is destroyed.  This does mean most likely you will die (in some sense) when you get Teleported but it may only be in the same discontinuity sense that you lose consciousness as you sleep, then awake the next morning with usually no memory of your dreamless sleep!  Check section 4.3 here.

This topic continues to have new research shedding light on the true answer of whether it's possible or not from many sources, Quantum Physics, Neuroscience, Computer Science (Information Theory/Quantum Computers), Philosophy...etc.  So I'll continue to follow it but I haven't seen anything conclusively rule it out, quite the opposite in fact!  However, I'll say again, from an Engineering standpoint it's nearly an impossible task given our current state of technology but let's keep in mind our Smart Phones have the computational power of Supercomputers back in the 1990's that were the size of entire rooms!

PS  I spent a lot of time thinking about (Quantum) Teleportation but actually the idea from Star Trek that would likely have the biggest impact on our daily lives is The Replicator, it's like the ultimate 3D copier, it can create dishes (with plates), drinks, pretty much any consumer product!  For those that don't delve into deep science it might sound just as hard as the Teleportation to create these things but the amazing fact is that it's soooo much easier!  We're getting pretty close!  Just think of how much time could be saved, not going shopping, not cooking (except on rare occasions where you'd like to!), not cleaning up after etc!!  Here's where we are at today on this topic, we don't need it to work exactly like it did in Star Trek (they were just very imaginative/smart guesses at the future) so we don't need to try and convert Energy to Matter via E=MC^2, it's much easier to use Nanotechnology and rearrange molecules etc.  Turns out though that Scientists are close to even achieving this energy/matter conversion in the labratory via the "fancy physics" way so who knows (but this approach to Replication would take far longer than the Molecular Assembler)!