Chapter 9: Quantum Teleportation

Quantum teleportation might sound like something straight out of science fiction, but it's a real phenomenon in quantum science! In the context of quantum information science, teleportation is the process of transferring the properties of one quantum object to another, not by physically moving them, but by sharing their quantum states through a process involving entanglement and classical communication. 

For now we'll skip the nitty-gritty details of how specifically quantum teleportation is implemented and instead provide some intuition on how it works. Recall from Chapter 2: Entanglement that when two parties share an entangled state, they will find that measurements of the entangled state are correlated. For example, if Alice and Bob shares the bell state

then every time Alice measures 0, so will Bob. Similarly every time Alice measures 1, so too will Bob measure 1.

Therefore if Alice has a third qubit in state α|0⟩+ β|1⟩, she can transfer this state to Bob's by using the correlations of the entangled state that Alice and Bob share. However, communicating through this "quantum channel" (i.e. measurement of the entangled state) is not sufficient. This is because the state that Alice and Bob measures are random. There is an equally likely chance that Alice/Bob measures either 0 or 1, so it is not possible to deterministically share information.

As it turns out, Alice and Bob need to share an additional 2 bits of information classically (e.g. over a telephone line or the internet) in order to deterministically transfer the state of Alice's qubit to Bob.

This result may seem a bit underwhelming. After all, we still need to communicate information classically. However, the fact that we can easily teleport a quantum state from Alice to Bob should really be quite surprising! Classically, our intuition would be to first measure the values a and b of Alice's qubit, send them to Bob, and then Bob can easily recreate Alice's state. However, it is not possible to determine the value of α or β with a single measurement because a quantum measurement collapses Alice's state. We would have to make many measurements of Alice's state to gather enough statistics to piece together the values of α and β. However, using the quantum teleportation scheme, we can transfer Alice's state to Bob even if Alice only has a single copy of the state.

So why is quantum teleportation called "teleportation" and not "quantum state copying." While Bob can deterministically recreate Alice's state it is at the cost of destroying the state of Alice's qubit. In other words, after the teleportation scheme, Alice's qubit is no longer in a meaningful state. Hence the state (or rather the information of the state) is destroyed at Alice's node and recreated at Bob's --- teleported!

The fact the teleported state at Alice's end is destroyed is not a flaw of the quantum teleportation algorithm that we used but is in fact a law of quantum science. Called the "No-Cloning Theorem," researchers have mathematically shown that it is not possible to copy the state of a qubit to another qubit without destroying the first qubit. In other words, it is not possible to clone the state of one qubit onto another. [Editor's note: so rest assured, if you ever enter a quantum teleportation machine in the future, you will not accidentally create a clone. However, the original copy of you will be destroyed...]

While quantum teleportation is a cool concept, it also has practical applications. For instance, in photonic quantum computing, quantum teleportation can be used to "teleport" probabilistic two-qubit gates at the beginning of circuits, enabling deterministic computation when sufficiently entangled states can be prepared. Indeed, quantum teleportation plays a crucial role in many advancing quantum technologies.