Quantum Teleportation

Move an unknown qubit’s state across the room without copying it — using a shared entangled pair and two ordinary bits of news.

Quantum Computing · Lesson 27 · 11 min read

Last lesson left us with a puzzle: you can’t copy an unknown quantum state, so how do you ever move one from Alice to Bob? You can’t fax it (that’s copying), and handing over the physical qubit isn’t always possible. The answer is one of the most famous — and most misunderstood — results in the field: quantum teleportation. Despite the sci-fi name, nothing travels faster than light and no matter is beamed anywhere. Hold the question: how can you transfer an unknown state to a distant qubit without copying it and without breaking the cosmic speed limit?

The setup: a pre-shared entangled pair

Teleportation needs one thing arranged in advance: Alice and Bob share an entangled pair of qubits (recall entanglement from Module 1 — two qubits with linked outcomes, one held by each). Alice also holds the mystery qubit whose unknown state she wants to send. The entangled pair is the channel: it’s a pre-established correlation between the two labs. On its own it carries no message — but combined with the right operations, it becomes the bridge the unknown state crosses. Think of the entangled pair as rails laid down ahead of time; the state is the train that will run on them.

The trick: a joint measurement, then two classical bits

Alice performs a joint measurement on her two qubits — the mystery one and her half of the entangled pair — together. This does two things: it destroys the original state on her side (so no copy ever exists — no-cloning is respected), and it yields two ordinary bits of result. Because of the entanglement, Bob’s far qubit is now almost the original state — but scrambled in one of four ways, and only Alice’s two bits say which. She sends those two bits over any normal channel (phone, internet). Bob applies the matching fix-up operation, and his qubit becomes the exact original state. The state moved; it was never copied.

The three ingredients, in order:
1. Resource: Alice & Bob pre-share an entangled pair (one qubit each).
2. Alice jointly measures her mystery qubit + her half → gets 2 classical bits, and her originals are destroyed.
3. She phones Bob the 2 bits; Bob applies the corresponding correction → his qubit is now the original state, exactly. No qubit was copied and no matter traveled.

Why it doesn’t break the speed of light

Here’s the part everyone gets wrong. The instant Alice measures, Bob’s qubit does jump to one of the four scrambled versions — but Bob can’t tell which, and a random scramble is useless to him. To unscramble it he needs Alice’s two classical bits, and those travel no faster than light, by phone or fiber like any message. So no information arrives before the classical bits do: teleportation is exactly as fast as ordinary communication, no faster. Entanglement provides the correlation; the classical message provides the key to use it. Neither alone transmits anything — which is precisely why the universe’s speed limit stays intact.

Why the “instant” jump carries no message:
1. Alice measures; Bob’s qubit instantly becomes one of 4 scrambled versions of the original.
2. Bob looks at his qubit — but any of the 4 looks equally random to him; he learns nothing about the original yet.
3. Only when Alice’s 2 classical bits arrive (at light speed or slower) does Bob know which of the 4 unscramblings to apply.
4. He applies it and recovers the exact state. The useful information arrived with the classical bits — not a moment sooner — so no faster-than-light signaling occurred.