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Exp erimental Quantum Telep ortation
Dik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter, and Anton Zeilinger Institut fur Experimentalphysik, Universitat, Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria (Decemb er 10, 1997)
ABSTRACT
Quantum telep ortation-the transmission and reconstruction over arbitrary distances of the state of a quantum system- is demonstarted ex- p erimentally. During telep ortation, an initial photon which carries the p olarization that is to b e transferred and one of a pair of entangled pho- tons are sub jected to a measurement such that the second photon of the entangled pair acquires the p olarization of the initial photon. This later photon can b e arbitrarily far away from the ini- tial one. Quantum telep ortation will b e a critical ingredient for quantum computation networks.
The dream of telep ortation is to b e able to travel by simply reapp earing at some distant lo cation. Any ob ject to b e telep orted can b e fully characterized by its prop- erties, which in classical physics can b e determined by measurement. To make a copy of that ob ject at a dis- tant lo cation one do es not need the original parts and pieces; all that is needed is to send the scanned infor- mation so that it can b e used for reconstructing the ob- ject. But how precisely can this b e a true copy of the original? What if these parts and pieces are electrons, atoms and molecules? What happ ens to their individual quantum prop erties, which according to the Heisenb erg's uncertainty principle can not b e measured with arbitrary precision? Bennett et al. [1] have suggested that it is p ossible to transfer the quantum state of a particle onto another particle, the pro cess of quantum telep ortation, provided one do es not get any information ab out the state in the course of this transformation. This requirement can b e ful lled by using entanglement, the essential feature of quantum mechanics [2]. It describ es correlations b etween quantum systems much stronger than any classical cor- relation could b e. The p ossibility of transferring quantum information is one of the cornerstones of the emerging eld of quan- tum communication and quantum computation [3]. Al- though there is fast progress in the theoretical descrip- tion of quantum information pro cessing, the diculties in handling quantum systems have not allowed an equal advance in the exp erimental realization of the new pro- p osals. Besides the promising developments of quan- tum cryptography [4] (the rst provably secure way to
send secret messages), we have only recently succeeded in demonstrating the p ossibility of quantum dense co ding [5], a way to quantum mechanically enhance data com- pression. The main reason for this slow exp erimental progress is that, although there exist metho ds to pro- duce pairs of entangled photons [6], entanglement has b een demonstrated for atoms [7] only very recently and it has not b een p ossible thus far to pro duce entangled states of more than two quanta. Here we rep ort the rst exp erimental veri cation of quantum telep ortation. By pro ducing pairs of entangled photons by the pro cess of parametric down-conversion and using two-photon interferometry for analysing entan- glement, we could transfer a quantum prop erty (in our case the p olarization state) from one photon to another. The metho ds develop ed for this exp eriment will b e of great imp ortance b oth for exploring the eld of quantum communication as well as for future exp eriments on the foundations of quantum mechanics.
THE PROBLEM
To make the problem of transferring quantum infor- mation clearer supp ose that Alice has some particle in a
certain quantum state j i and she wants Bob, at a dis-
tant lo cation, to have a particle in that state. There is certainly the p ossibility to send Bob the particle directly. But supp ose that the communication channel b etween Alice and Bob is not go o d enough to preserve the neces- sary quantum coherence or supp ose that this would take
to o much time, which could easily b e the case if j i is
the state of a more complicated or massive ob ject. Then, what strategy can Alice and Bob pursue? As mentioned ab ove, no measurement that Alice can
p erform on j i will b e sucient for Bob to reconstruct
the state b ecause the state of a quantum system cannot b e fully determined by measurements. Quantum systems are so evasive b ecause they can b e in a sup erp osition of several states at the same time. A measurement on the quantum system will force it into only one of these states; this is often referred to as the pro jection p ostulate. We can illustrate this imp ortant quantum feature by taking a single photon, which can b e horizontally or vertically
p olarised, indicated by the states j$i and jli. It can
even b e p olarised in the general sup erp osition of these two states
j i = j$i + jli ; (1)
were and are two complex numb ers satisfying j j^2 +
j j^2 = 1. To place this example in a more general setting
we can replace the states j$i and jli in Eq.(1) by j 0 i and
j 1 i, which refer to the states of any two-state quantum
system. Sup erp ositions of j 0 i and j 1 i are called qubits
to signify the new p ossibilities intro duced by quantum physics into information science [8].
If a photon in state j i passes through a p olarizing
b eamsplitter, a device that re ects (transmits) horizon- tally (vertically) p olarized photons, it will b e found in
the re ected (transmitted) b eam with probability j j^2
(j j^2 ). Then the general state j i has b een pro jected
either onto j$i or onto jli by the action of the measure-
ment. We conclude that the rules of quantum mechanics, in particular the pro jection p ostulate, make it imp ossible
for Alice to p erform a measurement on j i by which she
would obtain all the information necessary to reconstruct the state.
THE CONCEPT OF QUANTUM TELEPORTATION
Although the pro jection p ostulate in quantum me- chanics seems to bring Alice's attempts to provide Bob
with the state j i to a halt, it was realised by Bennett
et al. [1] that precisely this pro jection p ostulate enables
telep ortation of j i from Alice to Bob. During telep orta-
tion Alice will destroy the quantum state at hand while Bob receives the quantum state, with neither Alice nor
Bob obtaining information ab out the state j i. A key
role in the telep ortation scheme is played by an entangled ancillary pair of particles which will b e initially shared by Alice and Bob. Supp ose particle 1 which Alice wants to telep ort is in
the initial state j i 1 = j$i 1 + jli 1 (Fig. 1a), and the
entangled pair of particles 2 and 3 shared by Alice and Bob is in the state:
23 =^
p
(j$i 2 jli 3 jli 2 j$i 3 ) : (2)
That entangled pair is a single quantum system in an
equal sup erp ositon of the states j$i 2 jli 3 and jli 2 j$i 3.
The entangled state contains no information on the indi- vidual particles; it only indicates that the two particles will b e in opp osite states. The imp ortant prop erty of an entangled pair is that as so on as a measurement on one
of the particles pro jects it, say, onto j$i the state of the
other one is determined to b e jli, and vice versa. How
could a measurement on one of the particles instanta- neously in uence the state of the other particle which, can b e arbitrarily far away?! Einstein, among many other distinguished physicists, could simply not accept this "Sp o oky action at a distance". By this prop erty of entangled states has now b een demonstrated by numer- ous exp eriments (for reviews, see refs [9] [10]). The telep ortation scheme works as follows. Alice has
the particle 1 in the initial state j i 1 and particle 2. Par-
ticle 2 is entangled with particle 3 in the hands of Bob.
The essential p oint is to p erform a sp eci c measurement on particles 1 and 2 which pro jects them onto the entan- gled state:
12 =^
p
(j$i 1 jli 2 jli 1 j$i 2 ) : (3)
This is only one of four p ossible maximally entangled states into which any state of two particles can b e decom- p osed. The pro jection of an arbitrary state of two parti- cles onto the basis of the four states is called a Bell-state measurement. The state given in Eq.(3) distinguishes it- self from the three other maximally entangled states by the fact that it changes sign up on interchanging particle 1 and particle 2. This unique anti-symmetric feature of
j i 12 will play an imp ortant role in the exp erimental
identi cation, that is, in measurements of this state. Quantum physics predicts [1] that once particle 1 and
2 are pro jected onto j i 12 , particle 3 is instantaneously
pro jected into the initial state of particle 1. The reason for this is as follows. Because we observe particles 1 and
2 in the state j i 12 we know that whatever the state of
particle 1 is, particle 2 must b e in the opp osite 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
j i 23 , which means that particle 2 is also orthogonal
to particle 3. This is only p ossible if particle 3 is in the same state as particle 1 was initially! The nal state of particle 3 is therefore:
j i 3 = j$i 3 + jli 3 : (4)
Note that during the Bell-state measurement particle 1 loses its identity b ecause it b ecomes entangled with par-
ticle 2. Therefore the state j i 1 is destroyed on Alice's
side during telep ortation. This result (Eq.(4)) deserves some further comments. The transfer of quantum information from particle 1 to particle 3 can happ en over arbitrary distances, hence the name telep ortation. Exp erimentally, quantum entangle- ment has b een shown to survive over distances of the order of 10 km [11]. We note that in the telep ortation scheme it is not necessary for Alice to know where Bob is. Furthermore, the initial state of particle 1 can b e com- pletely unknown not only to Alice but to anyone. It could even b e quantum mechanically completely unde ned at the time the Bell-state measurement takes place. This is the case when, as already remarked by Bennett et al [1], particle 1 itself is a memb er of an entangled pair and therefore has no well-de ned prop erties on its own. This ultimately leads to entanglement swapping [12] [13]. It is also imp ortant to notice that the Bell-state mea- surement do es not reveal any information on the prop er- ties of any of the particles. This is the very reason why quantum telep ortation using coherent two-particle sup er- p ositions works, while any measurement on one-particle sup erp ositions would fail. The fact that no information whatso ever on either particle is gained is also the reason
Outside the region of telep ortation photon 1 and 2 each will go either to f1 or to f2 indep endent of one another. The probability to have a coincidence b etween f1 and f2 is therefore 50%, which is twice as high as inside the region of telep ortation. Photon 3 should not have a well- de ned p olarization b ecause it is part of an entangled pair. Therefore, d1 and d2 have b oth a 50% chance of receiving photon 3. This simple argument yields a
25% probability b oth for the 45 analysis (d1f1f2 coin-
cidences) and for the +45 analysis (d2f1f2 coincidences) outside the region of telep ortation. Figure 3 summarises the predictions as function of the delay. Successful tele- p ortation of the +45 p olarization state is then charac-
terized by a decrease to zero in the 45 analysis (Fig.
3a), and by a constant value for the +45 analysis (Fig. 3b). The theoretical prediction of Fig. 3 may easily b e un- dersto o d by realizing that at zero delay there is a decrease to half in the coincidence rate for the two detectors of the Bell-state analyser, f1 and f2, as compared to outside the region of telep ortation. Therefore, if the p olarization of photon 3 were completely uncorrelated to the others the three-fold coincidence should also show this dip to half. That the right state is telep orted is indicated by the fact that the dip go es to zero in Fig. 3a and it is lled to a at curve in Fig. 3b. We note that ab out as likely as pro duction of photons 1, 2, and 3 is emission of two pairs of down-converted photons by a single source. Although there is no photon coming from the second source (photon 1 is absent), there will still b e a signi cant contribution to the three-fold coincidence rates. These coincidences have nothing to do with telep ortation and can b e identi ed by blo cking the path of photon 1. The probability for this pro cess to yield spurious two- and three-fold coincidences can b e estimated by taking into account the exp erimental parameters. The exp eri- mentally determined value for the p ercentage of spurious
three-fold coincidences is 68% 1%. In the exp erimental
graphs of Fig. 4 we have subtracted the exp erimentally determined spurious coincidences. The exp erimental results for telep ortation of photons p olarized under +45 is shown in the left column of Fig. 4; Fig. 4a and b should b e compared with the theoretical predictions as shown in Fig. 3. The strong decrease in
the 45 analysis, and the constant signal for the +45
analysis, indicate that photon 3 is p olarized along the direction of photon 1, con rming telep ortation.
The results for photon 1 p olarized at 45 demon-
strate that telep ortation works for a complete basis for p olarization states (right-hand column of Fig. 4). To rule out any classical explanation for the exp erimental results, we have pro duced further con rmation that our pro cedure works by additional exp eriments. In these ex- p eriments we telep orted photons linearly p olarized at 0 and at 90 , and also telep orted circularly p olarized pho- tons. The exp erimental results are summarized in Table 1, where we list the visibility of the dip in three-fold co-
incidences, which o ccurs for analysis orthogonal to the input p olarization. polarization visibility
circular 0 : 57 0 : 02
As mentioned ab ove, the values for the visibilities are obtained after subtracting the o set caused by spurious three-fold coincidences. These can exp erimentally b e ex- cluded by conditioning the three-fold coincidences on the detection of photon 4, which e ectively pro jects photon 1 into a single-particle state. We have p erformed this four- fold coincidence measurement for the case of telep orta- tion of the +45 and +90 p olarization states, that is, for two non-orthogonal states. The exp erimental results are
shown in Fig. 5. Visibilities of 70% 3% are obtained
for the dips in the orthogonal p olarization states! Here, these visibilities are directly the degree of p olarization of the telep orted photon in the right state. This proves that we demonstrated telep ortation of the quantum state of a single photon.
THE NEXT STEPS
In our exp eriment, we used pairs of p olarization en- tangled photons as pro duced by pulsed down-conversion and two-photon interferometric metho ds to transfer the p olarization state of one photon onto another one. But, telep ortation is by no means restricted to this system. In addition to pairs of entangled photons or entangled atoms [7] [21], one could imagine entangling photons with atoms or phonons with ions, and so on. Then telep ortation would allow us to transfer the state of, for example, fast- decohering, short-lived particles onto some more stable systems. This op ens the p ossibility of quantum memo- ries, where the information of incoming photons is stored on trapp ed ions, carefully shielded from the environment. Furthermore, with entanglement puri cation [22], a scheme of improving the quality of entanglement if it was degraded by decoherence during storage or transmission of the particles over noisy channels, it b ecomes p ossible to send the quantum state of a particle to some place, even if the available quantum channels are of very p o or quality and thus sending the particle itself would very probably destroy the fragile quantum state. The feasi- bility of preserving quantum states in a hostile environ- ment will have great advantages in the realm of quantum computation. The telep ortation scheme can b e used to provide links b etween quantum computeres. Quantum telep ortation is not only an imp ortant ingre- dient in quantum information tasks; it also allows new typ es of exp eriments and investigations on the founda- tions of quantum mechanics. As any arbitrary state can b e telep orted, so can the fully undetermined state of a
particle which is memb er of an entangled pair. Doing so, one transfers the entanglement b etween particles. This allows us not only to chain the transmission of quantum states over distances, where decoherence would have al- ready destroyed the state completely, but it also enables us to p erform test of Bell's theorem on particles which do not share any common past, a new step in the inves- tigation of the features of quantum mechanics. Last but not least, the discussion ab out the lo cal realistic charac- ter of nature could b e settled at all if one uses features of the exp eriment presented here to generate entanglement b etween more than two spatially separated particles [23] [24].
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ACKNOWLEDGEMENT
We thank Charles Bennett, Ignacio Cirac, John Rar- ity, Bill Wo otters, and Peter Zoller for discussions and Marek Zukowski for valuable suggestion concerning vari- ous asp ects of the exp eriments. This work was supp orted by the Austrian Science Foundation FWF, the Austrian Academy of Sciences and TMR program of the Europ ean Union.
Corresp ondence and requests for materials should b e addressed to D. B. (e-mail: Dik.Bouwmeester@uibk.ac.at).
FIG. 5. Four-fold coincidence rates (without background subtraction). Conditioning the three-fold coincidences as shown in Fig. 4 on the registration of photon 4 (see Fig. 1b) eliminates the spurious three-fold background. Graphs a and b show the four-fold coincidence measurements for the case of telep orta- tion of the +45 p olarization state, and graphs c and d show the results for the +90 p olarization state. The visibili ties , and thus the p olarizations of the telep orted photons, obtained without any background subtraction are 70% 3%. These re- sults for telep ortation of two non-orthogonal states prove that we demonstrated telep ortation of the quantum state of a sin- gle photon.
