Date: 2015-02-25

The 'no-cloning' theorem of quantum mechanics forbids the perfect copying of properties of photons or electrons. But quantum teleportation allows their flawless transfer — now even for two properties simultaneously.

Suppose you see a beautiful table in a museum and you would like to have the same one at home. What could you do? One strategy is to accurately measure all its properties — its form (length, height and width) and its appearance (material and colour) — and then reproduce an identical copy for your living room. But this 'measure-and-reproduce' strategy would fail if the table were a quantum particle, such as a photon or an electron orbiting an atomic nucleus. The no-cloning theorem^{1} of quantum mechanics tells us that it is impossible to copy such a particle perfectly. On page 516 of this issue, Wang *et al*.^{2} show how to get around this apparent limitation of quantum physics. In a beautiful extension of previous experiments, they demonstrate how to transfer the values of two properties of a photon — the spin angular momentum (the direction of the photon's electric field, generally referred to as polarization) and the orbital angular momentum (which depends on the field distribution) — through quantum teleportation onto another photon.

Quantum teleportation was proposed^{3} in 1993 and first demonstrated^{4} in 1997 for a single property of a photon (the polarization). It allows the flawless transfer of the unknown properties of an object onto a second object without contradicting the no-cloning theorem: the first object loses all its properties at the same time, that is, the properties are not 'copied' during quantum teleportation, they are transferred. However, the properties of the second object after this transfer remain unknown — all that is known is that they have been made identical to those of the first object before teleportation. What is more, the transfer does not happen instantaneously, a common mistake in the non-scientific literature.

In addition to the object (A) that carries the property to be teleported, quantum teleportation requires two more objects (B and C; Fig. 1). Objects B and C have to be entangled, which means that their properties are strongly correlated. For instance, the two photons B and C should have the same polarization, but the actual direction of their individual electric fields is not defined. Sounds weird? Just think, for example, that they are either both horizontally polarized or both vertically polarized, or both polarized at 45°. Photon A, whose polarization, say, will be teleported onto photon C, is measured jointly with photon B in a way that reveals, loosely speaking, the difference in the electric fields' directions without revealing the individual directions. What would we learn from getting, for instance, zero as the result? From the outcome of this comparative measurement, we know that the polarization of photon A equals that of photon B. Furthermore, from the entanglement of photons B and C, we know that the polarization of photon B equals that of photon C. Hence, we find that the electric field of photon C must now point in the same direction as that of photon A before the measurement.

Figure 1: Teleportation of photon polarization and orbital angular momentum.

Photon A, whose polarization and orbital angular momentum are shown with a small arrow and an ellipse, respectively, is measured jointly with photon B, which is quantum-mechanically entangled with photon C. This act consists of: a comparative measurement of the polarizations of photons A and B (CM-P); a non-destructive verification that exactly one photon exits this measurement in path 1, and hence exactly one photon exits in path 2, given that two photons entered CM-P; and a comparative measurement of the orbital angular momenta of photons A and B (CM-OAM). The measurements result in the teleportation (that is, the transfer) of photon A's properties onto photon C. The transfer may require rotations of photon C's (unknown) polarization and orbital angular momentum, as determined by the outcomes of the comparative measurements. Wang *et al*.^{2} have implemented all but the rotation steps in this transfer scheme. Teleporting the polarization alone does not require the non-destructive measurement, the CM-OAM, nor the rotation of photon C's orbital angular momentum.

Note that the outcome of the joint measurement could also have been different: for example, A and B are orthogonally polarized. Similar reasoning to that used before would lead to the conclusion that photon C's electric field is rotated by 90° with respect to that of photon A. Therefore, rotating it back would allow one to perfectly recover the original polarization encoded in photon A. In short, the joint measurement, possibly followed by a well-defined rotation of the (unknown) polarization of photon C, has allowed the teleporting (transferring) of the polarization property from photon A to photon C without error.

To demonstrate the teleportation of two properties, Wang and colleagues started with a single photon (photon A in Fig. 1) prepared in a combination of polarization and orbital angular momentum. Using high-intensity laser pulses that pass through a crystal, they also created a photon pair (photons B and C in Fig. 1) in a 'hyper-entangled' state, in which the photons are simultaneously entangled in the two properties to be teleported. Making two joint measurements (one per property) that compared the polarizations and the orbital angular momenta of photon A and photon B then led to the teleportation of photon A's properties onto photon C.

The biggest challenge for the researchers was the concatenation of the two joint measurements. It required, as an intermediate step, the verification that exactly one photon exited the first measurement (that of polarization) in each of the two possible paths leading to the second measurement (that of angular orbital momenta), without destroying the photons. The non-destructive detection of, say, a photon in path 1 can be implemented by teleporting its orbital angular momentum onto another photon, which then enters the second joint measurement. This is because teleportation not only transfers a property from one photon to another, but also indicates that a photon existed. And, given that two photons entered (and hence left) the first comparative measurement, the non-destructive detection of a photon in path 1 also indicates that one photon was present in path 2 — exactly the requirement for the verification step. This step needed another pair of photons (not shown in Fig. 1) entangled in their orbital angular momenta.

An interesting question is whether the demonstrated method for the teleportation of two properties can be generalized to more properties. The authors affirm that this is possible in principle. However, the probability of the required joint measurements leading to a useful outcome becomes smaller and smaller as the number of properties (and thus of joint measurements) increases. Although the probability is half in the case of standard (single-property) teleportation, it is 1/32 for two properties, as shown for the first time by Wang and co-workers. Furthermore, it decreases to 1/4,096 when teleporting an object that is described by three properties. Adding photons and photon detectors may increase the efficiency^{5}, but this adds even more complexity to an already difficult measurement.

Even without these additional photons, the joint measurement becomes increasingly challenging as the number of properties increases: in the teleportation of two properties, a 'one-property teleporter' is used, and in the teleportation of three properties, a 'two-property teleporter' and a 'one-property teleporter' would be needed. You can guess what is required for the teleportation of *N* properties. Yet, Wang and colleagues' demonstration is an important step in understanding, and showcasing, one of the most profound and puzzling predictions of quantum physics. It may serve as a powerful building block for future quantum networks, which generally require teleportation units for the transmission of quantum data.

References

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2. *et al*. Nature 518, 516–519 (2015).

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4. *et al*. Nature 390, 575–579 (1997).

5. Phys. Rev. A 84, 042331 (2011).