Free quantum tool · Level: First-year university and up
Quantum teleportation, two ways
Pick a state, pick what Alice measured, and watch Bob end up holding exactly what you chose. The same fact is drawn twice.
Try this on the tool above
- Set θ to 70° and φ to 40°, then click through all four outcomes. Bob's sphere lands on Alice's every time and the match reads 1,00.
- Turn on Bob before he corrects and pick outcome 01. The two spheres now disagree and the match falls, which is those two classical bits doing real work.
- Turn on how likely each outcome is. All four sit at 25%, whatever state you dial in, so Alice learns nothing about what she is sending.
Teleportation moves an unknown qubit state from Alice to Bob using one shared entangled pair and two classical bits. Alice measures her qubit together with her half of the pair, gets one of four results at random, and sends those two bits to Bob, who applies X, Z, both or nothing. Nothing outruns light, because Bob's qubit is useless until those bits arrive, and Alice's original is destroyed by her own measurement.
The usual mistake
The state jumps across to Bob the instant Alice measures.
Something does change at his end straight away, but he cannot use it. Until Alice's two bits arrive he cannot tell which of four states he is holding, and all four look identical to every measurement he can make. Those bits travel by ordinary means at ordinary speed.
What actually crosses the gap
Not a particle. Bob's qubit never leaves his lab, and the entangled pair was shared before anyone knew what would be sent. Two ordinary classical bits make the trip.
Turn on the outcome probabilities and all four sit at 25% for every input state you can dial in. Alice learns nothing about what she is sending, which is also why an eavesdropper who copies her two bits learns nothing.
The correction is doing real work
Pick outcome 01 and turn on Bob before he corrects. His qubit is Alice's state with an X applied, and the two spheres visibly disagree. Switch the layer off again and the correction lands it exactly.
This is where the instant-transmission reading falls apart. Bob genuinely holds something the moment Alice measures, and without her two bits he cannot tell which of four things it is.
The same thing as a bent wire
Turn on the diagram. The entangled pair is a cup, a wire that goes out and comes back. Alice's Bell measurement is a cap, a wire that folds over. Together they make a zig-zag: right, back to the left, then forward again to Bob.
The rule that finishes the proof is that a zig-zag pulls straight. A wire with a kink in it is still a wire, so what comes out at Bob is what went in at Alice. As algebra that is a page of index work. As a diagram it is one move.
Why this is not copying
The no-cloning theorem says no operation can duplicate an unknown quantum state. Teleportation stays inside that rule because Alice's copy is gone: her measurement destroyed it, and that destruction is the reason the protocol is allowed to exist at all.
Check it on the sliders. At no point do two qubits carry the same state, and the moment Bob has it, Alice does not.
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Frequently asked questions
- How does quantum teleportation work?
- Alice and Bob share an entangled pair in advance. Alice measures the qubit she wants to send together with her half of that pair, which gives one of four random results and destroys the original. She sends those two bits to Bob, he applies the matching correction, and his half becomes the state Alice had.
- Does teleportation beat the speed of light?
- No. Bob's qubit is in one of four states and he cannot tell which until Alice's two classical bits reach him, and those travel no faster than anything else. Without them, every measurement he can make gives the same statistics regardless of what Alice sent.
- Is anything physically moved?
- No matter and no energy travels between Alice and Bob during the protocol. The particles were brought together earlier to be entangled, and after that only two classical bits are sent. What transfers is the state, not the thing carrying it.
- Why is the original destroyed?
- Because Alice has to measure it, and measuring collapses the state. That is also what keeps no-cloning intact: if the original survived you would end up with two copies of an unknown state, which quantum mechanics does not allow.