The word teleportation suggests science fiction: a person dissolving on one planet and reappearing on another. Quantum teleportation is something narrower and in some ways more surprising. Quantum teleportation transfers the quantum state of one particle onto another distant particle, without sending the particle itself. No matter moves, nothing goes faster than light, and the original state is destroyed along the way.

The problem it solves

Suppose Ana holds a photon in some unknown polarization state and wants Ben, far away, to have a photon in exactly that state. She cannot simply measure it and phone him the answer. A single measurement gives one random result and destroys the rest of the information, and by the no-cloning theorem she cannot make copies to measure many times. Teleportation shows a way around this, provided Ana and Ben already share entanglement.

The 1993 proposal

Quantum teleportation was proposed in 1993 by six physicists: Charles Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres and William Wootters. Their scheme has three ingredients. First, Ana and Ben share an entangled pair, one particle each. Second, Ana performs a joint measurement on two particles together: the photon whose state she wants to send and her half of the entangled pair. This kind of joint test, called a Bell-state measurement, asks how the two particles are related to each other rather than what either one is doing alone. It has four possible outcomes, each equally likely.

Third, Ana sends the outcome to Ben by ordinary means. Ana must send Ben two bits of ordinary information, enough to say which of the four outcomes she got. Depending on the message, Ben applies one of four simple operations to his particle, such as rotating its polarization. After that, his particle is in exactly the state Ana's original photon was in.

What does and does not happen

It is worth being precise. Ana's measurement scrambles her original photon, so the original state is destroyed at Ana's end, which is why teleportation does not violate the no-cloning theorem. At no moment do two copies exist. Before Ben receives Ana's message, his particle's state is random from his point of view, an equal mix of four possibilities that tells him nothing. So teleportation cannot beat light, because Ben's particle is useless until the ordinary message arrives. And neither Ana nor Ben ever learns what the state was. It passed from one particle to the other without being read.

The entangled pair is used up in the process. To teleport another state, they need a fresh pair. This is why researchers treat shared entanglement as a resource to be produced, distributed and spent.

From the lab to orbit

The first teleportation experiments, in 1997, were carried out by Anton Zeilinger's group in Innsbruck and by Francesco De Martini's group in Rome, using photons. Since then, states have been teleported between atoms, between ions and across ever longer distances. In 2017 a Chinese team led by Pan Jianwei, a former student of Zeilinger's, used the Micius satellite to teleport photon states from a ground station in Tibet to the satellite in orbit, over distances of up to about 1,400 kilometers.

Entanglement swapping

A close cousin of teleportation does something even stranger. Suppose Ana and a middle station share one entangled pair, and Ben and the middle station share another. The middle station performs a Bell-state measurement on its two particles. In entanglement swapping, a joint measurement on two particles leaves their distant partners, which have never met, entangled with each other. The Innsbruck group demonstrated it in 1998. It is the trick that the Delft Bell test of 2015 used, and it is the basis for proposed quantum repeaters that would extend entanglement across long networks, a topic for QUAN 203.

Swapping highlights a rule called the monogamy of entanglement. If two particles are maximally entangled with each other, neither can be entangled with any third particle at all. In swapping, the middle particles give up their entanglement with Ana's and Ben's particles, and that is what lets the outer two become linked. Entanglement can be moved, but it cannot be shared freely.

Worked example: teleporting a polarization

Ana holds a photon polarized at some angle she does not know; call it the message photon. She and Ben share an entangled pair made moments earlier, Ana keeping one photon and Ben the other. Ana brings the message photon and her half of the pair together and performs a Bell-state measurement on them. She gets one of four outcomes, say the third, and the message photon's polarization is no longer recoverable at her end.

She sends Ben a short text: the number three, which takes two bits. Ben looks up his instructions: for outcome three, rotate the polarization in a fixed way. He does, and his photon now carries the exact polarization of the original message photon, an angle that neither of them knows.

Had Ben acted before the text arrived, guessing an outcome, he would be wrong three times in four, and his photon would be no better than random.