Teleportation versus cloning

In Chapter 5, we showed that a qubit can’t be cloned. That is, if you start with a qubit in a certain state, you can’t use that qubit to make a second qubit that’s in the very same state. But in this chapter, Alice starts out with a qubit in a certain state, and Bob ends up with a qubit in that same state. What’s going on here?

The trick in teleportation is that Alice measures her qubit. She destroys her qubit’s superposition and sacrifices the qubit’s original state to Bob. You can see this measurement in the fourth-from-last gate in Figure 6.8. Without a destructive act on Alice’s qubit, the transfer of state would be impossible.

To bring this concept home, let’s revisit the equations in Chapter 5 and find out where that chapter’s No-Cloning Theorem turns into this chapter’s Yes-Teleporting-Possibility Theorem.

Let’s start with a capsule summary of the reasoning in Chapter...