Quantum teleportation allows the transfer of an arbitrary unknown quantum state — in principle over any distance. The sender and receiver need not have a good enough connection to be capable of transferring a fragile quantum state between them. Instead, the task is achieved by a double application of quantum entanglement. The sender doesn't even have to know which state is being teleported — and never has to know. To date, quantum teleportation has been realized with many different systems, including electrons, atoms and superconducting circuits. But as many of the early experiments were carried out with photons, in the following we will refer explicitly to the teleportation of photons, keeping in mind that the same argument also holds for the other systems.

Quantum state teleportation was first proposed in 1993 by Bennett et al. Back then, my immediate reaction was that we were years — if not decades — away from the realization of such a task. To my surprise, over time I learned that we were actually already developing the right tools for quantum teleportation. Our goal at that time had been to realize multiparticle entanglement. For our successful quantum teleportation in 1997, just the same tools were finally used.

It may be instructive and entertaining to consider for a moment the concept of teleportation in science fiction (think: “Beam me up, Scotty”). There, the principle is that somehow the object is scanned at the sending station. The information obtained about the object is then sent over to the receiving station where, based on that information, the object is reconstituted. It was noted that such a procedure would be impossible from the point of view of quantum mechanics, as there exists no measurement that determines the complete quantum state of an unknown system. This happens because any measurement introduces some uncontrollable disturbance to the quantum state, a fact related to the Heisenberg uncertainty principle. Thus, to make up for these problems, the creators of Star Trek invented the 'Heisenberg compensator' — a device that also cannot exist.

In fact, the solution came from quantum mechanics itself: quantum entanglement allows the transfer of a quantum state without that state being measured or observed. In principle, the procedure of quantum teleportation follows a rather clear concept, which I will discuss here in a way accessible for non-physicists.

One initially starts with the photon one wants to teleport. Actually, I should mention that in quantum teleportation it is the state of a quantum system that is teleported, rather than the system itself. So let us consider, for simplicity, the polarization state of a photon. The incoming 'teleportee' photon can have some arbitrary polarization, which can be completely unknown. This polarization is to be teleported by Alice to Bob. To prepare for teleportation, Alice and Bob share an auxiliary entangled pair of photons, which will serve as the bridge for teleportation.

Entanglement is the quantum concept that Erwin Schrödinger in 1935 called “not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought”. Two photons, or any two particles or systems, can be entangled in many different ways. One possible polarization entanglement is that the two photons exhibit the same linear polarization when measured. So, for example, when a random measurement signals that one photon is horizontally polarized, then the other photon will also show horizontal polarization, no matter how far away it is. One might simply guess that the two photons are created with the same polarization, but that would be false: it is the nature of entanglement that neither of the two photons carries any well-defined polarization before a measurement. As there is no connection between the two photons, Einstein dismissed the phenomenon of entanglement as “spooky action at a distance” — hoping for a future physics without it.

The next step is now crucial and somewhat tricky. Alice entangles her teleportee photon with her photon from the auxiliary entangled pair. When teleportation was proposed in 1993, no one knew how to entangle two independent particles, like our photons. The key to entangling two independent photons is to make them forfeit their identity, which can be achieved with beam splitters — semi-reflecting mirrors. Imagine two photons hitting a beam splitter; say one from the right and one from the left. Then, if they emerge at exactly the same time, one does not know — and one cannot even know, not even in principle — which photon exiting the beam splitter came from which direction.

As soon as Alice's original photon gets entangled with the photon from the auxiliary pair, it loses its well-defined polarization. In that moment, the information contained in Alice's state is instantly transferred to Bob's photon. This is not like faxing, where the original remains available.

As mentioned, Bob's photon immediately assumes the original state of Alice's input photon without any delay and even without any connection between the two systems at the moment of teleportation. The procedure is not in conflict with Einstein's relativity theory, which prohibits any information to be transferred faster than the speed of light. The reason for this is a rather subtle one. When Alice entangles the teleportee photon and her photon from the auxiliary entangled pair at the beam splitter, she is carrying out a measurement that projects them onto an entangled state. This type of measurement is called a Bell state measurement, after the Irish physicist John Bell. A Bell state measurement has only four possible different outcomes, one of which is chosen at random. In each case, Bob's photon contains the original information, but in an encoded way, depending on the specific entangled state obtained. Bob has not yet received any useful information about the original state, preventing any violation of relativity theory. In order for teleportation to finally succeed, Bob has to know Alice's Bell state measurement result — a transmission that is limited by the speed of light. Then, based on that information, Bob rotates the polarization of his photon accordingly and obtains the original state in all cases.

So far, quantum teleportation has been realized over distances of the order of 100 km on Earth. Recently, the quantum state of a photon was teleported from the ground station Ngari at an altitude of 5,047 m in the Tibetan mountains in western China to the quantum satellite Micius over a distance of up to 1,400 km (Fig. 1).

Figure 1: Quantum teleportation from the ground station Ngari at 5,047-m altitude to the quantum satellite Micius.
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The teleportation distance reached up to 1,400 km. Reproduced from Reproduced from J.-G. Ren et al., Nature 549, 70–73 (2017).

Today, quantum teleportation is no longer simply a curiosity. It is considered the way future quantum computers will talk to one another: any arbitrary quantum state that is the output of a quantum computer could be teleported directly to the input of another one. Actually, the receiving quantum computer could even start to work instantly on the input state, without knowing whether it's the correct one or not. And although the output of the computer will be useful only once Bob receives the classical result from Alice, there is still an important advantage in not having to wait to start the computation.

To cover distances larger than about 100 km using ground networks on Earth, one might be tempted to consider an amplifier to overcome losses. Such amplifiers cannot exist because of the no-cloning theorem, according to which perfect cloning of an unknown quantum state is not possible. The way to overcome this limitation is to employ entanglement swapping (Fig. 2), which was first realized in 1998 and can be considered the teleportation of an entangled state. Entanglement swapping is at the core of future quantum repeaters, which would also contain procedures of entanglement purification.

Figure 2: Long-distance entanglement swapping between the Canary Islands of La Palma and Tenerife.
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On La Palma, two entangled pairs are produced by Einstein–Podolsky–Rosen (EPR) sources. Photons 1 and 2, one from each pair, are subject to a Bell state measurement (BSM), following which the other two photons, 0 and 3, become entangled even as they do not interact in any way. Alice's photon is delayed by a 100-m glass fibre and measured on La Palma. Bob's photon is transmitted via telescopes over a 143-km free-space link to the Optical Ground Station operated by the European Space Agency on Tenerife. Adapted from T. Scheidl et al., Proc. Natl Acad. Sci. USA 107, 19708 (2010).

Besides their role in quantum communication, quantum teleportation and entanglement swapping are also very important for quantum computation. One can use quantum teleportation in quantum gates, for example, allowing fault-tolerant quantum computation, or, interestingly, one can even use quantum teleportation to teleport quantum gates. Some operations of that kind have already been demonstrated in various laboratories.

Another very interesting development is quantum teleportation and entanglement swapping in higher dimensions. That way, using orbital angular momentum states of photons, for example, more information per photon can be transferred.

It might not be an overstatement to say that a future Internet will contain, to a significant extent, quantum features, many of them based on quantum teleportation and entanglement swapping. To witness the excitement about these perspectives, one needs to look no further than the latest developments in laboratories around the world. Most of these applications were not foreseen twenty years ago. Likewise, it is certainly not overly optimistic to expect new interesting applications and further fundamental developments based on quantum teleportation and entanglement swapping in the future.