articles Experimental quantum teleportation Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter & Anton Zeilinger Institut fu¨r Experimentalphysik, Universita¨t Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum teleportation-the transmission and reconstruction over arbitrary distances of the state of a quantum system-is demonstrated experimentally. During teleportation, an initial photon which carries the polarization that is to be transferred and one of a pair of entangled photons are subjected to a measurement such that the second photon of the entangled pair acquires the polarization of the initial photon. This latter photon can be arbitrarily far away from the initial one. Quantum teleportation will be a critical ingredient for quantum computation networks. The dream of teleportation is to be able to travel by simply and she wants Bob, at a distant location, to have a particle in that reappearing at some distant location. An object to be teleported state. There is certainly the possibility of sending Bob the particle can be fully characterized by its properties, which in classical physics directly. But suppose that the communication channel between can be determined by measurement. To make a copy of that object at Alice and Bob is not good enough to preserve the necessary a distant location one does not need the original parts and pieces- quantum coherence or suppose that this would take too much all that is needed is to send the scanned information so that it can be time, which could easily be the case if | w is the state of a more used for reconstructing the object. But how precisely can this be a complicated or massive object. Then, what strategy can Alice and true copy of the original? What if these parts and pieces are Bob pursue? electrons, atoms and molecules? What happens to their individual As mentioned above, no measurement that Alice can perform quantum properties, which according to the Heisenberg's uncer- on |w will be sufficient for Bob to reconstruct the state because the tainty principle cannot be measured with arbitrary precision? state of a quantum system cannot be fully determined by measure- Bennett et al.1 have suggested that it is possible to transfer the ments. Quantum systems are so evasive because they can be in a quantum state of a particle onto another particle-the process of superposition of several states at the same time. A measurement on quantum teleportation-provided one does not get any informa- the quantum system will force it into only one of these states-this tion about the state in the course of this transformation. This is often referred to as the projection postulate. We can illustrate this requirement can be fulfilled by using entanglement, the essential important quantum feature by taking a single photon, which can be feature of quantum mechanics2. It describes correlations between horizontally or vertically polarized, indicated by the states | and | . quantum systems much stronger than any classical correlation It can even be polarized in the general superposition of these two could be. states The possibility of transferring quantum information is one of the cornerstones of the emerging field of quantum communication and jw ¼ aj þ bj ð1Þ quantum computation3. Although there is fast progress in the where a and b are two complex numbers satisfying jaj2 þ jbj2 ¼ 1. theoretical description of quantum information processing, the To place this example in a more general setting we can replace the difficulties in handling quantum systems have not allowed an states | and | in equation (1) by |0 and |1 , which refer to the equal advance in the experimental realization of the new proposals. states of any two-state quantum system. Superpositions of |0 and Besides the promising developments of quantum cryptography4 | 1 are called qubits to signify the new possibilities introduced by (the first provably secure way to send secret messages), we have quantum physics into information science8. only recently succeeded in demonstrating the possibility of quan- If a photon in state | w passes through a polarizing beamsplit- tum dense coding5, a way to quantum mechanically enhance data ter-a device that reflects (transmits) horizontally (vertically) compression. The main reason for this slow experimental progress polarized photons-it will be found in the reflected (transmitted) is that, although there exist methods to produce pairs of entangled beam with probability | a|2 (| b| 2). Then the general state | w has photons6, entanglement has been demonstrated for atoms only very been projected either onto | or onto | by the action of the recently7 and it has not been possible thus far to produce entangled measurement. We conclude that the rules of quantum mechanics, in states of more than two quanta. particular the projection postulate, make it impossible for Alice to Here we report the first experimental verification of quantum perform a measurement on | w by which she would obtain all the teleportation. By producing pairs of entangled photons by the information necessary to reconstruct the state. process of parametric down-conversion and using two-photon interferometry for analysing entanglement, we could transfer a The concept of quantum teleportation quantum property (in our case the polarization state) from one Although the projection postulate in quantum mechanics seems to photon to another. The methods developed for this experiment will bring Alice's attempts to provide Bob with the state |w to a halt, it be of great importance both for exploring the field of quantum was realised by Bennett et al.1 that precisely this projection postulate communication and for future experiments on the foundations of enables teleportation of |w from Alice to Bob. During teleportation quantum mechanics. Alice will destroy the quantum state at hand while Bob receives the quantum state, with neither Alice nor Bob obtaining information The problem about the state |w . A key role in the teleportation scheme is played To make the problem of transferring quantum information clearer, by an entangled ancillary pair of particles which will be initially suppose that Alice has some particle in a certain quantum state |w shared by Alice and Bob. Nature © Macmillan Publishers Ltd 1997 NATURE | VOL 390 | 11 DECEMBER 1997 575 articles Suppose particle 1 which Alice wants to teleport is in the initial far away? Einstein, among many other distinguished physicists, state jw 1 ¼ aj 1 þ bj 1 (Fig. 1a), and the entangled pair of could simply not accept this ``spooky action at a distance''. But this particles 2 and 3 shared by Alice and Bob is in the state: property of entangled states has now been demonstrated by numer- 1 ÿ ous experiments (for reviews, see refs 9, 10). jw 23 ¼ p j ð2Þ The teleportation scheme works as follows. Alice has the particle 1 2 2j 3 j 2j 3 in the initial state | w 1 and particle 2. Particle 2 is entangled with That entangled pair is a single quantum system in an equal particle 3 in the hands of Bob. The essential point is to perform a superposition of the states | 2| 3 and | 2| 3. The entangled specific measurement on particles 1 and 2 which projects them onto state contains no information on the individual particles; it only the entangled state: indicates that the two particles will be in opposite states. The 1 ÿ important property of an entangled pair is that as soon as a jw 12 ¼ p j 1j 2 j 1j 2 ð3Þ measurement on one of the particles projects it, say, onto | the 2 state of the other one is determined to be | , and vice versa. How This is only one of four possible maximally entangled states into could a measurement on one of the particles instantaneously which any state of two particles can be decomposed. The projection influence the state of the other particle, which can be arbitrarily of an arbitrary state of two particles onto the basis of the four states is called a Bell-state measurement. The state given in equation (3) distinguishes itself from the three other maximally entangled states by the fact that it changes sign upon interchanging particle 1 and particle 2. This unique antisymmetric feature of |w- 12 will play an important role in the experimental identification, that is, in mea- surements of this state. Quantum physics predicts1 that once particles 1 and 2 are projected into | w- 12, particle 3 is instantaneously projected into the initial state of particle 1. The reason for this is as follows. Because we observe particles 1 and 2 in the state |w- 12 we know that whatever the state of particle 1 is, particle 2 must be in the opposite state, that is, in the state orthogonal to the state of particle 1. But we had initially prepared particle 2 and 3 in the state |w- 23, which means that particle 2 is also orthogonal to particle 3. This is only possible if particle 3 is in the same state as particle 1 was initially. The final state of particle 3 is therefore: jw 3 ¼ aj 3 þ bj 3 ð4Þ We note that during the Bell-state measurement particle 1 loses its identity because it becomes entangled with particle 2. Therefore the state |w 1 is destroyed on Alice's side during teleportation. This result (equation (4)) deserves some further comments. The transfer of quantum information from particle 1 to particle 3 can happen over arbitrary distances, hence the name teleportation. Experimentally, quantum entanglement has been shown11 to survive over distances of the order of 10 km. We note that in the teleporta- tion scheme it is not necessary for Alice to know where Bob is. Furthermore, the initial state of particle 1 can be completely unknown not only to Alice but to anyone. It could even be quantum mechanically completely undefined at the time the Bell-state mea- surement takes place. This is the case when, as already remarked by Bennett et al.1, particle 1 itself is a member of an entangled pair and Figure 1 Scheme showing principles involved in quantum teleportation (a) and therefore has no well-defined properties on its own. This ultimately the experimental set-up (b). a, Alice has a quantum system, particle 1, in an initial leads to entanglement swapping12,13. state which she wants to teleport to Bob. Alice and Bob also share an ancillary It is also important to notice that the Bell-state measurement does entangled pair of particles 2 and 3 emitted by an Einstein­Podolsky­Rosen (EPR) not reveal any information on the properties of any of the particles. source. Alice then performs a joint Bell-state measurement (BSM) on the initial This is the very reason why quantum teleportation using coherent particle and one of the ancillaries, projecting them also onto an entangled state. two-particle superpositions works, while any measurement on one- After she has sent the result of her measurement as classical information to Bob, particle superpositions would fail. The fact that no information he can perform a unitary transformation (U) on the other ancillary particle resulting whatsoever is gained on either particle is also the reason why in it being in the state of the original particle. b, A pulse of ultraviolet radiation quantum teleportation escapes the verdict of the no-cloning passing through a nonlinear crystal creates the ancillary pair of photons 2 and 3. theorem14. After successful teleportation particle 1 is not available After retroflection during its second passage through the crystal the ultraviolet in its original state any more, and therefore particle 3 is not a clone pulse creates another pair of photons, one of which will be prepared in the initial but is really the result of teleportation. state of photon 1 to be teleported, the other one serving as a trigger indicating that A complete Bell-state measurement can not only give the result a photon to be teleported is under way. Alice then looks for coincidences after a that the two particles 1 and 2 are in the antisymmetric state, but with beam splitter BS where the initial photon and one of the ancillaries are equal probabilities of 25% we could find them in any one of the superposed. Bob, after receiving the classical information that Alice obtained a three other entangled states. When this happens, particle 3 is left in coincidence count in detectors f1 and f2 identifying the |w- 12 Bell state, knows that one of three different states. It can then be brought by Bob into the his photon 3 is in the initial state of photon 1 which he then can check using original state of particle 1 by an accordingly chosen transformation, polarization analysis with the polarizing beam splitter PBS and the detectors d1 independent of the state of particle 1, after receiving via a classical and d2. The detector p provides the information that photon 1 is under way. communication channel the information on which of the Bell-state Nature © Macmillan Publishers Ltd 1997 576 NATURE | VOL 390 | 11 DECEMBER 1997 articles results was obtained by Alice. Yet we note, with emphasis, that even the pump pulses had a duration of 200 fs at a repetition rate of if we chose to identify only one of the four Bell states as discussed 76 MHz. Observing the down-converted photons at a wavelength of above, teleportation is successfully achieved, albeit only in a quarter 788 nm and a bandwidth of 4 nm results in a coherence time of of the cases. 520 fs. It should be mentioned that, because photon 1 is also produced as part of an entangled pair, its partner can serve to Experimental realization indicate that it was emitted. Teleportation necessitates both production and measurement of How can one experimentally prove that an unknown quantum entangled states; these are the two most challenging tasks for any state can be teleported? First, one has to show that teleportation experimental realization. Thus far there are only a few experimental works for a (complete) basis, a set of known states into which any techniques by which one can prepare entangled states, and there other state can be decomposed. A basis for polarization states has exist no experimentally realized procedures to identify all four Bell just two components, and in principle we could choose as the basis states for any kind of quantum system. However, entangled pairs of horizontal and vertical polarization as emitted by the source. Yet this photons can readily be generated and they can be projected onto at would not demonstrate that teleportation works for any general least two of the four Bell states. superposition, because these two directions are preferred directions We produced the entangled photons 2 and 3 by parametric down- in our experiment. Therefore, in the first demonstration we choose conversion. In this technique, inside a nonlinear crystal, an incom- as the basis for teleportation the two states linearly polarized at -45 ing pump photon can decay spontaneously into two photons which, and +45 which are already superpositions of the horizontal and in the case of type II parametric down-conversion, are in the state vertical polarizations. Second, one has to show that teleportation given by equation (2) (Fig. 2)6. works for superpositions of these base states. Therefore we also To achieve projection of photons 1 and 2 into a Bell state we have demonstrate teleportation for circular polarization. to make them indistinguishable. To achieve this indistinguishability we superpose the two photons at a beam splitter (Fig. 1b). Then if Results they are incident one from each side, how can it happen that they In the first experiment photon 1 is polarized at 45 . Teleportation emerge still one on each side? Clearly this can happen if they are should work as soon as photon 1 and 2 are detected in the | w- 12 either both reflected or both transmitted. In quantum physics we state, which occurs in 25% of all possible cases. The | w- 12 state is have to superimpose the amplitudes for these two possibilities. identified by recording a coincidence between two detectors, f1 and Unitarity implies that the amplitude for both photons being f2, placed behind the beam splitter (Fig. 1b). reflected obtains an additional minus sign. Therefore, it seems If we detect a f1f2 coincidence (between detectors f1 and f2), then that the two processes cancel each other. This is, however, only photon 3 should also be polarized at 45 . The polarization of photon true for a symmetric input state. For an antisymmetric state, the two 3 is analysed by passing it through a polarizing beam splitter possibilities obtain another relative minus sign, and therefore they selecting +45 and -45 polarization. To demonstrate teleportation, constructively interfere15,16. It is thus sufficient for projecting only detector d2 at the +45 output of the polarizing beam splitter photons 1 and 2 onto the antisymmetric state | w- 12 to place should click (that is, register a detection) once detectors f1 and f2 detectors in each of the outputs of the beam splitter and to register click. Detector d1 at the -45 output of the polarizing beam splitter simultaneous detections (coincidence)17­19. should not detect a photon. Therefore, recording a three-fold To make sure that photons 1 and 2 cannot be distinguished by coincidence d2f1f2 (+45 analysis) together with the absence of a their arrival times, they were generated using a pulsed pump beam three-fold coincidence d1f1f2 (-45 analysis) is a proof that the and sent through narrow-bandwidth filters producing a coherence polarization of photon 1 has been teleported to photon 3. time much longer than the pump pulse length20. In the experiment, To meet the condition of temporal overlap, we change in small Figure 2 Photons emerging from type II down-conversion (see text). Photograph Figure 3 Theoretical prediction for the three-fold coincidence probability between taken perpendicular to the propagation direction. Photons are produced in pairs. the two Bell-state detectors (f1, f2) and one of the detectors analysing the A photon on the top circle is horizontally polarized while its exactly opposite teleported state. The signature of teleportation of a photon polarization state at partner in the bottom circle is vertically polarized. At the intersection points their +45 is a dip to zero at zero delay in the three-fold coincidence rate with the polarizations are undefined; all that is known is that they have to be different, detector analysing -45 (d1f1f2) (a) and a constant value for the detector analysis which results in entanglement. +45 (d2f1f2) (b). The shaded area indicates the region of teleportation. Nature © Macmillan Publishers Ltd 1997 NATURE | VOL 390 | 11 DECEMBER 1997 577 articles steps the arrival time of photon 2 by changing the delay between the Table 1 Visibility of teleportation in three fold coincidences first and second down-conversion by translating the retroflection Polarization Visibility mirror (Fig. 1b). In this way we scan into the region of temporal ............................................................................................................................................................................. overlap at the beam splitter so that teleportation should occur. +45 0:63 0:02 -45 0:64 0:02 Outside the region of teleportation, photon 1 and 2 each will go 0 0:66 0:02 either to f1 or to f2 independent of one another. The probability of 90 0:61 0:02 having a coincidence between f1 and f2 is therefore 50%, which is Circular 0:57 0:02 ............................................................................................................................................................................. twice as high as inside the region of teleportation. Photon 3 should not have a well-defined polarization because it is part of an entangled pair. Therefore, d1 and d2 have both a 50% chance of for the percentage of spurious three-fold coincidences is receiving photon 3. This simple argument yields a 25% probability 68% 1%. In the experimental graphs of Fig. 4 we have subtracted both for the -45 analysis (d1f1f2 coincidences) and for the +45 the experimentally determined spurious coincidences. analysis (d2f1f2 coincidences) outside the region of teleportation. The experimental results for teleportation of photons polarized Figure 3 summarizes the predictions as a function of the delay. under +45 are shown in the left-hand column of Fig. 4; Fig. 4a and Successful teleportation of the +45 polarization state is then b should be compared with the theoretical predictions shown in characterized by a decrease to zero in the -45 analysis (Fig. 3a), Fig. 3. The strong decrease in the -45 analysis, and the constant and by a constant value for the +45 analysis (Fig. 3b). signal for the +45 analysis, indicate that photon 3 is polarized along The theoretical prediction of Fig. 3 may easily be understood by the direction of photon 1, confirming teleportation. realizing that at zero delay there is a decrease to half in the The results for photon 1 polarized at -45 demonstrate that coincidence rate for the two detectors of the Bell-state analyser, f1 teleportation works for a complete basis for polarization states and f2, compared with outside the region of teleportation. There- (right-hand column of Fig. 4). To rule out any classical explanation fore, if the polarization of photon 3 were completely uncorrelated to for the experimental results, we have produced further confirmation the others the three-fold coincidence should also show this dip to that our procedure works by additional experiments. In these half. That the right state is teleported is indicated by the fact that the experiments we teleported photons linearly polarized at 0 and at dip goes to zero in Fig. 3a and that it is filled to a flat curve in Fig. 3b. 90 , and also teleported circularly polarized photons. The experi- We note that equally as likely as the production of photons 1, 2 mental results are summarized in Table 1, where we list the visibility and 3 is the emission of two pairs of down-converted photons by a of the dip in three-fold coincidences, which occurs for analysis single source. Although there is no photon coming from the first orthogonal to the input polarization. source (photon 1 is absent), there will still be a significant con- As mentioned above, the values for the visibilities are obtained after tribution to the three-fold coincidence rates. These coincidences subtracting the offset caused by spurious three-fold coincidences. have nothing to do with teleportation and can be identified by These can experimentally be excluded by conditioning the three-fold blocking the path of photon 1. coincidences on the detection of photon 4, which effectively projects The probability for this process to yield spurious two- and three- photon 1 into a single-particle state. We have performed this four- fold coincidences can be estimated by taking into account the fold coincidence measurement for the case of teleportation of the experimental parameters. The experimentally determined value +45 and +90 polarization states, that is, for two non-orthogonal Figure 4 Experimental results. Measured three-fold coincidence rates d1f1f2 Figure 5 Four-fold coincidence rates (without background subtraction). Con- (-45 ) and d2f1f2 (+45 ) in the case that the photon state to be teleported is ditioning the three-fold coincidences as shown in Fig. 4 on the registration of polarized at +45 (a and b) or at -45 (c and d). The coincidence rates are plotted as photon 4 (see Fig. 1b) eliminates the spurious three-fold background. a and b function of the delay between the arrival of photon 1 and 2 at Alice's beam splitter show the four-fold coincidence measurements for the case of teleportation of the (see Fig. 1b). The three-fold coincidence rates are plotted after subtracting the +45 polarization state; c and d show the results for the +90 polarization state. The spurious three-fold contribution (see text). These data, compared with Fig. 3, visibilities, and thus the polarizations of the teleported photons, obtained without together with similar ones for other polarizations (Table 1) confirm teleportation any background subtraction are 70% 3%. These results for teleportation of two for an arbitrary state. non-orthogonal states prove that we have demonstrated teleportation of the quantum state of a single photon. Nature © Macmillan Publishers Ltd 1997 578 NATURE | VOL 390 | 11 DECEMBER 1997 articles states. The experimental results are shown in Fig. 5. Visibilities of could be settled firmly if one used features of the experiment 70% 3% are obtained for the dips in the orthogonal polarization presented here to generate entanglement between more than two states. Here, these visibilities are directly the degree of polarization of spatially separated particles23,24. the teleported photon in the right state. This proves that we have Received 16 October; accepted 18 November 1997. demonstrated teleportation of the quantum state of a single photon. 1. Bennett,C. H. et al. Teleporting an unknownquantumstate via dual classic and Einstein-Podolsky- Rosen channels. Phys. Rev. Lett. 70, 1895­1899 (1993). The next steps 2. 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Zoller for discussions, tely, but it also enables us to perform a test of Bell's theorem on and M. Zukowski for suggestions about various aspects of the experiments. This work was supported by particles which do not share any common past, a new step in the the Austrian Science Foundation FWF, the Austrian Academy of Sciences, the TMR program of the European Union and the US NSF. investigation of the features of quantum mechanics. Last but not least, the discussion about the local realistic character of nature CorrespondenceandrequestsformaterialsshouldbeaddressedtoD.B.(e-mail:Dik.Bouwmeester@uibk. ac.at). Nature © Macmillan Publishers Ltd 1997 NATURE | VOL 390 | 11 DECEMBER 1997 579