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Quantum entanglement is 2 atoms that are paired together and when you stop one from spinning the other also stops with the same spin. Can you use these pairs to have faster-than-light (FTL) communication between 2 computers?

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As this is one of the first examples in Nielsen & Chuang, I'll go ahead and type out their explanation here for anyone else that is interested in entanglement for faster than light communication.

The following is an abridged version of Nielsen & Chuang section 1.3.7 entitled 'Example: quantum teleportation'

Quantum teleportation is a technique for moving quantum states around, even in the absence of a quantum communications channel linking the sender of the quantum state to the recipient.

Here’s how quantum teleportation works. Alice and Bob met long ago but now live far apart. While together they generated an EPR pair, each taking one qubit of the EPR pair (also known as Bell states) when they separated. Many years later, Bob is in hiding, and Alice’s mission, should she choose to accept it, is to deliver a qubit $\lvert \psi \rangle$ to Bob. She does not know the state of the qubit, and moreover can only send classical information to Bob. Should Alice accept the mission?

Intuitively, things look pretty bad for Alice. She doesn’t know the state $\lvert \psi \rangle$ of the qubit she has to send to Bob, and the laws of quantum mechanics prevent her from determining the state when she only has a single copy of $\lvert \psi \rangle$ in her possession. What’s worse, even if she did know the state $\lvert \psi \rangle$, describing it precisely takes an infinite amount of classical information since $\lvert \psi \rangle$ takes values in a continuous space. So even if she did know $\lvert \psi \rangle$, it would take forever for Alice to describe the state to Bob. It’s not looking good for Alice. Fortunately for Alice, quantum teleportation is a way of utilizing the entangled EPR pair in order to send $\lvert \psi \rangle$ to Bob, with only a small overhead of classical communication.

In outline, the steps of the solution are as follows: Alice interacts the qubit $\lvert \psi \rangle$ with her half of the EPR pair, and then measures the two qubits in her possession, obtaining one of four possible classical results, 00, 01, 10, and 11. She sends this information to Bob. Depending on Alice’s classical message, Bob performs one of four operations on his half of the EPR pair. Amazingly, by doing this he can recover the original state $\lvert \psi \rangle$!

Skipping some of the details...

First, doesn’t teleportation allow one to transmit quantum states faster than light? This would be rather peculiar because the theory of relativity implies that faster than light information transfer could be used to send information backward in time. Fortunately, quantum teleportation does not enable faster than light communication, because to complete the teleportation Alice must transmit her measurement result to Bob over a classical communications channel. The classical channel is limited by the speed of light, so it follows that quantum teleportation cannot be accomplished faster than the speed of light, resolving the apparent paradox.

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