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Nature © Macmillan Publishers Ltd 1997NATURE | VOL 390 | 11 DECEMBER 1997 575

articles

Experimental quantumteleportationDik Bouwmeester, Jian-Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter & Anton Zeilinger

Institut fur Experimentalphysik, Universitat Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria

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Quantum teleportation—the transmission and reconstruction over arbitrary distances of the state of a quantumsystem—isdemonstratedexperimentally.During teleportation,an initial photonwhichcarriesthepolarization that is tobe transferred and one of a pair of entangled photons are subjected to a measurement such that the second photon ofthe entangled pair acquires the polarization of the initial photon. This latter photon can be arbitrarily far away from theinitial one. Quantum teleportation will be a critical ingredient for quantum computation networks.

The dream of teleportation is to be able to travel by simplyreappearing at some distant location. An object to be teleportedcan be fully characterized by its properties, which in classical physicscan be determined by measurement. To make a copy of that object ata distant location one does not need the original parts and pieces—all that is needed is to send the scanned information so that it can beused for reconstructing the object. But how precisely can this be atrue copy of the original? What if these parts and pieces areelectrons, atoms and molecules? What happens to their individualquantum properties, which according to the Heisenberg’s uncer-tainty principle cannot be measured with arbitrary precision?

Bennett et al.1 have suggested that it is possible to transfer thequantum state of a particle onto another particle—the process ofquantum teleportation—provided one does not get any informa-tion about the state in the course of this transformation. Thisrequirement can be fulfilled by using entanglement, the essentialfeature of quantum mechanics2. It describes correlations betweenquantum systems much stronger than any classical correlationcould be.

The possibility of transferring quantum information is one of thecornerstones of the emerging field of quantum communication andquantum computation3. Although there is fast progress in thetheoretical description of quantum information processing, thedifficulties in handling quantum systems have not allowed anequal advance in the experimental realization of the new proposals.Besides the promising developments of quantum cryptography4

(the first provably secure way to send secret messages), we haveonly recently succeeded in demonstrating the possibility of quan-tum dense coding5, a way to quantum mechanically enhance datacompression. The main reason for this slow experimental progressis that, although there exist methods to produce pairs of entangledphotons6, entanglement has been demonstrated for atoms only veryrecently7 and it has not been possible thus far to produce entangledstates of more than two quanta.

Here we report the first experimental verification of quantumteleportation. By producing pairs of entangled photons by theprocess of parametric down-conversion and using two-photoninterferometry for analysing entanglement, we could transfer aquantum property (in our case the polarization state) from onephoton to another. The methods developed for this experiment willbe of great importance both for exploring the field of quantumcommunication and for future experiments on the foundations ofquantum mechanics.

The problemTo make the problem of transferring quantum information clearer,suppose that Alice has some particle in a certain quantum state |w�

and she wants Bob, at a distant location, to have a particle in thatstate. There is certainly the possibility of sending Bob the particledirectly. But suppose that the communication channel betweenAlice and Bob is not good enough to preserve the necessaryquantum coherence or suppose that this would take too muchtime, which could easily be the case if | w� is the state of a morecomplicated or massive object. Then, what strategy can Alice andBob pursue?

As mentioned above, no measurement that Alice can performon |w� will be sufficient for Bob to reconstruct the state because thestate of a quantum system cannot be fully determined by measure-ments. Quantum systems are so evasive because they can be in asuperposition of several states at the same time. A measurement onthe quantum system will force it into only one of these states—thisis often referred to as the projection postulate. We can illustrate thisimportant quantum feature by taking a single photon, which can behorizontally or vertically polarized, indicated by the states |⇥� and |⇤ �.It can even be polarized in the general superposition of these twostates

jw� ⇤ aj⇥� ⇧ bj ⇤ � �1⇥

where a and b are two complex numbers satisfying jaj2 ⇧ jbj2 ⇤ 1.To place this example in a more general setting we can replace thestates |⇥� and |⇤ � in equation (1) by |0� and |1�, which refer to thestates of any two-state quantum system. Superpositions of | 0� and| 1� are called qubits to signify the new possibilities introduced byquantum physics into information science8.

If a photon in state | w� passes through a polarizing beamsplit-ter—a device that reflects (transmits) horizontally (vertically)polarized photons—it will be found in the reflected (transmitted)beam with probability | a | 2 (| b | 2). Then the general state | w� hasbeen projected either onto | ⇥� or onto | ⇤ � by the action of themeasurement. We conclude that the rules of quantum mechanics, inparticular the projection postulate, make it impossible for Alice toperform a measurement on | w� by which she would obtain all theinformation necessary to reconstruct the state.

The concept of quantum teleportationAlthough the projection postulate in quantum mechanics seems tobring Alice’s attempts to provide Bob with the state |w� to a halt, itwas realised by Bennett et al.1 that precisely this projection postulateenables teleportation of |w� from Alice to Bob. During teleportationAlice will destroy the quantum state at hand while Bob receives thequantum state, with neither Alice nor Bob obtaining informationabout the state |w�. A key role in the teleportation scheme is playedby an entangled ancillary pair of particles which will be initiallyshared by Alice and Bob.

Nature © Macmillan Publishers Ltd 1997

articles

576 NATURE | VOL 390 | 11 DECEMBER 1997

Suppose particle 1 which Alice wants to teleport is in the initialstate jw�1 ⇤ aj ⇥ �1 ⇧ bj ⇤ �1 (Fig. 1a), and the entangled pair ofparticles 2 and 3 shared by Alice and Bob is in the state:

jw� �23 ⇤1

2j⇥�2j ⇤ �3 � j ⇤ �2j⇥�3 �2⇥

That entangled pair is a single quantum system in an equalsuperposition of the states | ⇥�2 | ⇤ �3 and | ⇤ �2 | ⇥�3. The entangledstate contains no information on the individual particles; it onlyindicates that the two particles will be in opposite states. Theimportant property of an entangled pair is that as soon as ameasurement on one of the particles projects it, say, onto |⇥� thestate of the other one is determined to be | ⇤ �, and vice versa. Howcould a measurement on one of the particles instantaneouslyinfluence the state of the other particle, which can be arbitrarily

far away? Einstein, among many other distinguished physicists,could simply not accept this ‘‘spooky action at a distance’’. But thisproperty of entangled states has now been demonstrated by numer-ous experiments (for reviews, see refs 9, 10).

The teleportation scheme works as follows. Alice has the particle 1in the initial state | w�1 and particle 2. Particle 2 is entangled withparticle 3 in the hands of Bob. The essential point is to perform aspecific measurement on particles 1 and 2 which projects them ontothe entangled state:

jw� �12 ⇤1

2j⇥�1j ⇤ �2 � j ⇤ �1j⇥�2 �3⇥

This is only one of four possible maximally entangled states intowhich any state of two particles can be decomposed. The projectionof an arbitrary state of two particles onto the basis of the four statesis called a Bell-state measurement. The state given in equation (3)distinguishes itself from the three other maximally entangled statesby the fact that it changes sign upon interchanging particle 1 andparticle 2. This unique antisymmetric feature of |w−�12 will play animportant role in the experimental identification, that is, in mea-surements of this state.

Quantum physics predicts1 that once particles 1 and 2 areprojected into | w−�12, particle 3 is instantaneously projected intothe initial state of particle 1. The reason for this is as follows. Becausewe observe particles 1 and 2 in the state |w−�12 we know that whateverthe state of particle 1 is, particle 2 must be in the opposite state, thatis, in the state orthogonal to the state of particle 1. But we hadinitially prepared particle 2 and 3 in the state |w−�23, which meansthat particle 2 is also orthogonal to particle 3. This is only possible ifparticle 3 is in the same state as particle 1 was initially. The final stateof particle 3 is therefore:

jw�3 ⇤ aj⇥�3 ⇧ bj ⇤ �3 �4⇥

We note that during the Bell-state measurement particle 1 loses itsidentity because it becomes entangled with particle 2. Therefore thestate |w�1 is destroyed on Alice’s side during teleportation.

This result (equation (4)) deserves some further comments. Thetransfer of quantum information from particle 1 to particle 3 canhappen over arbitrary distances, hence the name teleportation.Experimentally, quantum entanglement has been shown11 to surviveover 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 completelyunknown not only to Alice but to anyone. It could even be quantummechanically completely undefined at the time the Bell-state mea-surement takes place. This is the case when, as already remarked byBennett et al.1, particle 1 itself is a member of an entangled pair andtherefore has no well-defined properties on its own. This ultimatelyleads to entanglement swapping12,13.

It is also important to notice that the Bell-state measurement doesnot reveal any information on the properties of any of the particles.This is the very reason why quantum teleportation using coherenttwo-particle superpositions works, while any measurement on one-particle superpositions would fail. The fact that no informationwhatsoever is gained on either particle is also the reason whyquantum teleportation escapes the verdict of the no-cloningtheorem14. After successful teleportation particle 1 is not availablein its original state any more, and therefore particle 3 is not a clonebut is really the result of teleportation.

A complete Bell-state measurement can not only give the resultthat the two particles 1 and 2 are in the antisymmetric state, but withequal probabilities of 25% we could find them in any one of thethree other entangled states. When this happens, particle 3 is left inone of three different states. It can then be brought by Bob into theoriginal state of particle 1 by an accordingly chosen transformation,independent of the state of particle 1, after receiving via a classicalcommunication channel the information on which of the Bell-state

Figure 1 Scheme showing principles involved in quantum teleportation (a) and

the experimental set-up (b). a, Alice has a quantum system, particle 1, in an initial

state which she wants to teleport to Bob. Alice and Bob also share an ancillary

entangled pair of particles 2 and 3 emitted by an Einstein–Podolsky–Rosen (EPR)

source. Alice then performs a joint Bell-state measurement (BSM) on the initial

particle and one of the ancillaries, projecting them also onto an entangled state.

After she has sent the result of her measurement as classical information to Bob,

he canperform aunitary transformation (U) on the otherancillaryparticle resulting

in it being in the state of the original particle. b, A pulse of ultraviolet radiation

passing through a nonlinear crystal creates the ancillary pair of photons 2 and 3.

After retroflection during its second passage through the crystal the ultraviolet

pulse creates another pair of photons, one of which will be prepared in the initial

state of photon 1 to be teleported, the otherone servingas a trigger indicating that

a photon to be teleported is under way. Alice then looks for coincidences after a

beam splitter BS where the initial photon and one of the ancillaries are

superposed. Bob, after receiving the classical information that Alice obtained a

coincidence count in detectors f1 and f2 identifying the |w−�12 Bell state, knows that

his photon 3 is in the initial state of photon 1 which he then can check using

polarization analysis with the polarizing beam splitter PBS and the detectors d1

and d2. The detector p provides the information that photon 1 is under way.

Nature © Macmillan Publishers Ltd 1997

articles

576 NATURE | VOL 390 | 11 DECEMBER 1997

Suppose particle 1 which Alice wants to teleport is in the initialstate jw�1 ⇤ aj ⇥ �1 ⇧ bj ⇤ �1 (Fig. 1a), and the entangled pair ofparticles 2 and 3 shared by Alice and Bob is in the state:

jw� �23 ⇤1

2j⇥�2j ⇤ �3 � j ⇤ �2j⇥�3 �2⇥

That entangled pair is a single quantum system in an equalsuperposition of the states | ⇥�2 | ⇤ �3 and | ⇤ �2 | ⇥�3. The entangledstate contains no information on the individual particles; it onlyindicates that the two particles will be in opposite states. Theimportant property of an entangled pair is that as soon as ameasurement on one of the particles projects it, say, onto |⇥� thestate of the other one is determined to be | ⇤ �, and vice versa. Howcould a measurement on one of the particles instantaneouslyinfluence the state of the other particle, which can be arbitrarily

far away? Einstein, among many other distinguished physicists,could simply not accept this ‘‘spooky action at a distance’’. But thisproperty of entangled states has now been demonstrated by numer-ous experiments (for reviews, see refs 9, 10).

The teleportation scheme works as follows. Alice has the particle 1in the initial state | w�1 and particle 2. Particle 2 is entangled withparticle 3 in the hands of Bob. The essential point is to perform aspecific measurement on particles 1 and 2 which projects them ontothe entangled state:

jw� �12 ⇤1

2j⇥�1j ⇤ �2 � j ⇤ �1j⇥�2 �3⇥

This is only one of four possible maximally entangled states intowhich any state of two particles can be decomposed. The projectionof an arbitrary state of two particles onto the basis of the four statesis called a Bell-state measurement. The state given in equation (3)distinguishes itself from the three other maximally entangled statesby the fact that it changes sign upon interchanging particle 1 andparticle 2. This unique antisymmetric feature of |w−�12 will play animportant role in the experimental identification, that is, in mea-surements of this state.

Quantum physics predicts1 that once particles 1 and 2 areprojected into | w−�12, particle 3 is instantaneously projected intothe initial state of particle 1. The reason for this is as follows. Becausewe observe particles 1 and 2 in the state |w−�12 we know that whateverthe state of particle 1 is, particle 2 must be in the opposite state, thatis, in the state orthogonal to the state of particle 1. But we hadinitially prepared particle 2 and 3 in the state |w−�23, which meansthat particle 2 is also orthogonal to particle 3. This is only possible ifparticle 3 is in the same state as particle 1 was initially. The final stateof particle 3 is therefore:

jw�3 ⇤ aj⇥�3 ⇧ bj ⇤ �3 �4⇥

We note that during the Bell-state measurement particle 1 loses itsidentity because it becomes entangled with particle 2. Therefore thestate |w�1 is destroyed on Alice’s side during teleportation.

This result (equation (4)) deserves some further comments. Thetransfer of quantum information from particle 1 to particle 3 canhappen over arbitrary distances, hence the name teleportation.Experimentally, quantum entanglement has been shown11 to surviveover 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 completelyunknown not only to Alice but to anyone. It could even be quantummechanically completely undefined at the time the Bell-state mea-surement takes place. This is the case when, as already remarked byBennett et al.1, particle 1 itself is a member of an entangled pair andtherefore has no well-defined properties on its own. This ultimatelyleads to entanglement swapping12,13.

It is also important to notice that the Bell-state measurement doesnot reveal any information on the properties of any of the particles.This is the very reason why quantum teleportation using coherenttwo-particle superpositions works, while any measurement on one-particle superpositions would fail. The fact that no informationwhatsoever is gained on either particle is also the reason whyquantum teleportation escapes the verdict of the no-cloningtheorem14. After successful teleportation particle 1 is not availablein its original state any more, and therefore particle 3 is not a clonebut is really the result of teleportation.

A complete Bell-state measurement can not only give the resultthat the two particles 1 and 2 are in the antisymmetric state, but withequal probabilities of 25% we could find them in any one of thethree other entangled states. When this happens, particle 3 is left inone of three different states. It can then be brought by Bob into theoriginal state of particle 1 by an accordingly chosen transformation,independent of the state of particle 1, after receiving via a classicalcommunication channel the information on which of the Bell-state

Figure 1 Scheme showing principles involved in quantum teleportation (a) and

the experimental set-up (b). a, Alice has a quantum system, particle 1, in an initial

state which she wants to teleport to Bob. Alice and Bob also share an ancillary

entangled pair of particles 2 and 3 emitted by an Einstein–Podolsky–Rosen (EPR)

source. Alice then performs a joint Bell-state measurement (BSM) on the initial

particle and one of the ancillaries, projecting them also onto an entangled state.

After she has sent the result of her measurement as classical information to Bob,

he canperform aunitary transformation (U) on the otherancillaryparticle resulting

in it being in the state of the original particle. b, A pulse of ultraviolet radiation

passing through a nonlinear crystal creates the ancillary pair of photons 2 and 3.

After retroflection during its second passage through the crystal the ultraviolet

pulse creates another pair of photons, one of which will be prepared in the initial

state of photon 1 to be teleported, the otherone servingas a trigger indicating that

a photon to be teleported is under way. Alice then looks for coincidences after a

beam splitter BS where the initial photon and one of the ancillaries are

superposed. Bob, after receiving the classical information that Alice obtained a

coincidence count in detectors f1 and f2 identifying the |w−�12 Bell state, knows that

his photon 3 is in the initial state of photon 1 which he then can check using

polarization analysis with the polarizing beam splitter PBS and the detectors d1

and d2. The detector p provides the information that photon 1 is under way.

Polarization Entanglement

cristais

2

1

laser

{ {

crystal 1 crystal 2

|�⇥ = 1�2(| ⇤⇥1| ⇤⇥2 + | �⇥1| �⇥2)

crystals

Simplest example of a maximally entangled state

pump laser polarized at 45°

Two-photon Interference

crystal

BS

s

i 1

2

4 possibilities

beam splitter

Hong, Ou and Mandel (1987)

Two-photon Interference

crystal

BS

s

i 1

2

4 possibilities

Interference

Photon bunching

beam splitter

Hong, Ou and Mandel (1987)

Two-photon interference

a

b

cd

a† �!p

T c† + ip

1� T d†

b† �!p

T d† + ip

1� T c†

Beam Splitter, T

Hong, Ou, Mandel PRL 59 2044 (1987).

beam splitter transformation


a

b

cd

a† �!p

T c† + ip

1� T d†

b† �!p

T d† + ip

1� T c†

a†b† �! T c†d† � (1� T )c†d† + ip

T (1� T )h(c†)2 + (d†)2

i

Beam Splitter, T




a

b

cd

a† �!p

T c† + ip

1� T d†

b† �!p

T d† + ip

1� T c†

a†b† �! T c†d† � (1� T )c†d† + ip

T (1� T )h(c†)2 + (d†)2

i

a†b† �! (2T � 1)c†d† + ip

T (1� T )h(c†)2 + (d†)2

i

Beam Splitter, T




a

b

cd

a† �!p

T c† + ip

1� T d†

b† �!p

T d† + ip

1� T c†

a†b† �! T c†d† � (1� T )c†d† + ip

T (1� T )h(c†)2 + (d†)2

i

a†b† �! (2T � 1)c†d† + ip

T (1� T )h(c†)2 + (d†)2

i

Beam Splitter, T

a†b† �! i

2

h(c†)2 + (d†)2

i50/50 BS!T=1/2

Two-photon interference, photon bunching



BELL-STATE MEASUREMENT

Projection in the Bell-basis is an important primitive in many protocols in quantum communication and computation

(teleportation, quantum gates, dense coding, etc)

H| i 0/10/1

Bell-stateAnalyzer

1

2

ψ-ψ+ Φ+Φ-

| i

| ±i =1p2

(|Hi1|V i2 ± |V i1|Hi2)

|�±i =1p2

(|Hi1|Hi2 ± |V i1|V i2)Bell

States

BELL-STATE MEASUREMENT50/50 BSPBS(H/V) |�±i =

1p2(a†Hb†H ± a†V b†V )|vaci

PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:



PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:

BS transforms as:

a†Hb†H �!i

2(a†Ha†H + b†Hb†H)

a†V b†V �!i

2(a†V a†V + b†V b†V )

Photons in same output of BS



|�±i �! i

2p

2(a†Ha†H ± a†V a†V + b†Hb†H ± b†V b†V )|vaci

PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:

BS transforms as:

a†Hb†H �!i

2(a†Ha†H + b†Hb†H)

a†V b†V �!i

2(a†V a†V + b†V b†V )

Photons in same output of BS

BELL-STATE MEASUREMENT50/50 BSPBS(H/V)

PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:

BS transforms as:

| ±i =1p2(a†Hb†V ± a†V b†H)|vaci


PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:

BS transforms as:


a†Hb†V �!i

2(a†Ha†V + b†Hb†V ) + a†Hb†V � a†V b†H

a†V b†H �!i

2(a†Ha†V + b†Hb†V ) + a†V b†H � a†Hb†V


PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:

BS transforms as:


a†Hb†V �!i


a†V b†H �!i


| �i �! 1p2(a†Hb†V � a†V b†H)|vaci


PBS(H/V)

a

b

ba aH

aV

bV

bH

Consider states:

BS transforms as:


a†Hb†V �!i


a†V b†H �!i


| +i �! ip2(a†Ha†V + b†Hb†V )|vaci

BELL STATE MEASUREMENT

• With linear optics alone, and no additional auxiliary system, we can distinguish at most 3 classes of Bell states (ex. ψ-,ψ+,Φ±)

state events

• ψ- aHbV, aVbH

• ψ+ aHaV, bHbV

• Φ± aHaH, aVaV, bHbH, bVbV

Braunstein and Mann PRA (1995), Calsamiglia et al. PRA (1999) Lutkenhaus et al PRA (1999)

APPLICATIONS: DENSE CODING

VOLUME 76, NUMBER 25 P HY S I CA L REV I EW LE T T ER S 17 JUNE 1996

FIG. 1. Experimental setup for quantum dense coding. Be-cause of the nature of the Si-avalanche photodiodes, the exten-sion shown in the inset of Fig. 4 is necessary for identifyingtwo-photon states in one of the outputs.

degenerate noncollinear type-II down-conversion in anonlinear BBO crystal. A UV beam ⇤l ≠ 351 nm⌅from an argon-ion laser is down-converted into pairs ofphotons ⇤l ≠ 702 nm⌅ with orthogonal polarization. Weobtained the entangled state jC1⇥ after compensationof birefringence in the BBP crystal along two distinctemission directions (carefully selected by 2 mm irises,1.5 m away from the crystal [10]). One beam was firstdirected to Bob’s encoding station, the other directly toAlice’s Bell-state analyzer; in the alignment procedureoptical trombones were employed to equalize the pathlengths to well within the coherence length of the down-converted photons ⇤,c � 100 mm⌅, in order to observethe two-photon interference.For polarization encoding, the necessary transformation

of Bob’s particle was performed using a half-wave retar-dation plate for changing the polarization and a quarter-wave plate to generate the polarization-dependent phaseshift [11]. The beam manipulated in this way in Bob’s en-coding station was then combined with the other beam atAlice’s Bell-state analyzer. It consisted of a single beamsplitter followed by two-channel polarizers in each of itsoutputs and proper coincidence analysis between four sin-gle photon detectors.Such a configuration allows one to distinguish between

the Bell states due to the different outcomes of the in-terference at the beam splitter and the subsequent polar-ization analysis. The spatial part of the state determines

the photon statistics behind the (polarization insensitive)beam splitter. This results either in both photons leavingthe beam splitter via the same output beam for a symmet-ric spatial part or in one photon exiting into each outputfor an antisymmetric spatial component of the state [12].Since only the state jC2⇥ has an antisymmetric spatialpart, only this state will be registered by coincidence de-tection between the different outputs of the beam splitter(i.e., coincidence between detectors DH and DV 0 or be-tween DH 0 and DV ). For the remaining three states, bothphotons exit into the same output port of the beam splitter.The state jC1⇥ can easily be distinguished from the othertwo due to the different polarizations of the two photons,giving, behind the two-channel polarizer, a coincidencebetween detectors DH and DV or between DH 0 and DV 0 .The two states jF1⇥ and jF2⇥ both result in a two-photonstate being absorbed by a single detector and thus cannotbe distinguished. Table I gives an overview of the dif-ferent manipulations and detection probabilities of Bob’sencoder and Alice’s receiver.The experiments were performed by first setting the

output state of the source such that the state jC1⇥ leftBob’s encoder when both retardation plates were setto vertical orientation, the other Bell states could thenbe generated with the respective settings (Table I). Tocharacterize the interference observable at Alice’s Bell-state analyzer, we varied the path length difference D ofthe two beams with the optical trombone. For D ¿ ,c nointerference occurs, and one obtains classical statistics forthe coincidence count rates at the detectors. For optimalpath-length tuning ⇤D ≠ 0⌅, interference enables one toread the encoded information. Figures 2 and 3 show thedependence of the coincidence rates CHV ⇤�⌅ and CHV 0

⇤⇥⌅ on the path length difference for jC1⇥ and jC2⇥,respectively (the rates CH 0V 0 and CH 0V display analogousbehavior; we use the notation CAB for the coincidencerate between detectors DA and DB). At D ≠ 0, CHVreaches its maximum for jC1⇥ (Fig. 2) and vanishes(aside from noise) for jC2⇥ (Fig. 3). CHV 0 displays theopposite dependence and clearly signifies jC2⇥. Theresults of these measurements imply that, if both photonsare detected, we can identify the state jC1⇥ with areliability of 95% and the state jC2⇥ with 93%.The performance of the dense coding transmission is

influenced not only by the quality of the interference

TABLE I. Overview of possible manipulations and detection events of the quantum dense coding experiment with correlated pho-tons (we use h to denote the state of a photon in the mode towards detector DH , etc.).

Bob’s settingl⇧2 l⇧4 State sent State at output of Bell-state analyzer Alice’s registration events

0± 0± jC1⇥ ⌃hy 1 h0y0 1 yh 1 y0h0⌥⇧2 Coincidence between DH and DV or DH 0 and DV 0

0± 90± jC2⇥ ⌃hy0 2 h0y0 1 y0h 2 yh0⌥⇧2 Coincidence between DH and DV 0 or DH 0 and DV45± 0± jF1⇥ ⌃hh 1 yy 1 h0h0 1 y0y0⌥⇧2 2 photons in either DH , DV , DH 0 , or DV 0

45± 90± jF2⇥ ⌃hh 2 yy 1 h0h0 1 y0y0⌥⇧2 2 photons in either DH , DV , DH 0 , or DV 0

4657

| �i =1p2

(|Hi1|V i2 � |V i1|Hi2)

| ±i =1p2

(|Hi1|V i2 ± |V i1|Hi2)

|�±i =1p2

(|Hi1|Hi2 ± |V i1|V i2)

|��i = X2| �i| +i = �Z2| �i

|�+i = Z2X2| �i

Alice Recieves qubit 1, later Bob sends qubit 2.

Bob can transmit 2 bits of information (I, X, Z, ZX) by manipulating/sending qubit 2. Alice performs Bell-state Measurement

Bennett and Weisner, PRL (1992).

Mattle et al, PRL (1996).

APPLICATIONS: DENSE CODING

VOLUME 76, NUMBER 25 P HY S I CA L REV I EW LE T T ER S 17 JUNE 1996

FIG. 1. Experimental setup for quantum dense coding. Be-cause of the nature of the Si-avalanche photodiodes, the exten-sion shown in the inset of Fig. 4 is necessary for identifyingtwo-photon states in one of the outputs.

degenerate noncollinear type-II down-conversion in anonlinear BBO crystal. A UV beam ⇤l ≠ 351 nm⌅from an argon-ion laser is down-converted into pairs ofphotons ⇤l ≠ 702 nm⌅ with orthogonal polarization. Weobtained the entangled state jC1⇥ after compensationof birefringence in the BBP crystal along two distinctemission directions (carefully selected by 2 mm irises,1.5 m away from the crystal [10]). One beam was firstdirected to Bob’s encoding station, the other directly toAlice’s Bell-state analyzer; in the alignment procedureoptical trombones were employed to equalize the pathlengths to well within the coherence length of the down-converted photons ⇤,c � 100 mm⌅, in order to observethe two-photon interference.For polarization encoding, the necessary transformation

of Bob’s particle was performed using a half-wave retar-dation plate for changing the polarization and a quarter-wave plate to generate the polarization-dependent phaseshift [11]. The beam manipulated in this way in Bob’s en-coding station was then combined with the other beam atAlice’s Bell-state analyzer. It consisted of a single beamsplitter followed by two-channel polarizers in each of itsoutputs and proper coincidence analysis between four sin-gle photon detectors.Such a configuration allows one to distinguish between

the Bell states due to the different outcomes of the in-terference at the beam splitter and the subsequent polar-ization analysis. The spatial part of the state determines

the photon statistics behind the (polarization insensitive)beam splitter. This results either in both photons leavingthe beam splitter via the same output beam for a symmet-ric spatial part or in one photon exiting into each outputfor an antisymmetric spatial component of the state [12].Since only the state jC2⇥ has an antisymmetric spatialpart, only this state will be registered by coincidence de-tection between the different outputs of the beam splitter(i.e., coincidence between detectors DH and DV 0 or be-tween DH 0 and DV ). For the remaining three states, bothphotons exit into the same output port of the beam splitter.The state jC1⇥ can easily be distinguished from the othertwo due to the different polarizations of the two photons,giving, behind the two-channel polarizer, a coincidencebetween detectors DH and DV or between DH 0 and DV 0 .The two states jF1⇥ and jF2⇥ both result in a two-photonstate being absorbed by a single detector and thus cannotbe distinguished. Table I gives an overview of the dif-ferent manipulations and detection probabilities of Bob’sencoder and Alice’s receiver.The experiments were performed by first setting the

output state of the source such that the state jC1⇥ leftBob’s encoder when both retardation plates were setto vertical orientation, the other Bell states could thenbe generated with the respective settings (Table I). Tocharacterize the interference observable at Alice’s Bell-state analyzer, we varied the path length difference D ofthe two beams with the optical trombone. For D ¿ ,c nointerference occurs, and one obtains classical statistics forthe coincidence count rates at the detectors. For optimalpath-length tuning ⇤D ≠ 0⌅, interference enables one toread the encoded information. Figures 2 and 3 show thedependence of the coincidence rates CHV ⇤�⌅ and CHV 0

⇤⇥⌅ on the path length difference for jC1⇥ and jC2⇥,respectively (the rates CH 0V 0 and CH 0V display analogousbehavior; we use the notation CAB for the coincidencerate between detectors DA and DB). At D ≠ 0, CHVreaches its maximum for jC1⇥ (Fig. 2) and vanishes(aside from noise) for jC2⇥ (Fig. 3). CHV 0 displays theopposite dependence and clearly signifies jC2⇥. Theresults of these measurements imply that, if both photonsare detected, we can identify the state jC1⇥ with areliability of 95% and the state jC2⇥ with 93%.The performance of the dense coding transmission is

influenced not only by the quality of the interference

TABLE I. Overview of possible manipulations and detection events of the quantum dense coding experiment with correlated pho-tons (we use h to denote the state of a photon in the mode towards detector DH , etc.).

Bob’s settingl⇧2 l⇧4 State sent State at output of Bell-state analyzer Alice’s registration events

0± 0± jC1⇥ ⌃hy 1 h0y0 1 yh 1 y0h0⌥⇧2 Coincidence between DH and DV or DH 0 and DV 0

0± 90± jC2⇥ ⌃hy0 2 h0y0 1 y0h 2 yh0⌥⇧2 Coincidence between DH and DV 0 or DH 0 and DV45± 0± jF1⇥ ⌃hh 1 yy 1 h0h0 1 y0y0⌥⇧2 2 photons in either DH , DV , DH 0 , or DV 0

45± 90± jF2⇥ ⌃hh 2 yy 1 h0h0 1 y0y0⌥⇧2 2 photons in either DH , DV , DH 0 , or DV 0

4657

| �i =1p2

(|Hi1|V i2 � |V i1|Hi2)

| ±i =1p2

(|Hi1|V i2 ± |V i1|Hi2)

|�±i =1p2

(|Hi1|Hi2 ± |V i1|V i2)

|��i = X2| �i| +i = �Z2| �i

|�+i = Z2X2| �i

Alice Recieves qubit 1, later Bob sends qubit 2.

Bob can transmit 2 bits of information (I, X, Z, ZX) by manipulating/sending qubit 2. Alice performs Bell-state Measurement

Bennett and Weisner, PRL (1992).

Mattle et al, PRL (1996).

log23=1.58 bits/photon, with linear optics

Quantum Teleportation

Alice

Bob

12

3

Bennett et al., PRL 70 1895 (1993).

ψ-η


|⌘i1 = a|0i1 + b|1i1

Alice

Bob

12

3


ψ-η


| �i23 =1p2(|0i2|1i3 � |1i2|0i3)|⌘i1 = a|0i1 + b|1i1

Alice

Bob

12

3


ψ-η

|�i123 =1p2(a|0i1 + b|1i1)(|0i2|1i3 � |1i2|0i3)


| �i23 =1p2(|0i2|1i3 � |1i2|0i3)|⌘i1 = a|0i1 + b|1i1

Alice

Bob

12

3


ψ-η

|�i123 =1p2(a|0i1 + b|1i1)(|0i2|1i3 � |1i2|0i3)

=1p2(a|0i1|0i2|1i3 � a|0i1|1i2|0i3 + b|1i1|0i2|1i3 + b|1i1|1i2|0i3)


| �i23 =1p2(|0i2|1i3 � |1i2|0i3)|⌘i1 = a|0i1 + b|1i1

Alice

Bob

12

3


ψ-η


|�±i =1p2(|0i|0i± |1i|1i)

| ±i =1p2(|0i|1i± |1i|0i)

Bell States:


|�±i =1p2(|0i|0i± |1i|1i)

| ±i =1p2(|0i|1i± |1i|0i)

Bell States:

=1p2

|�+i12 + |��i12


|�±i =1p2(|0i|0i± |1i|1i)

| ±i =1p2(|0i|1i± |1i|0i)

Bell States:

=1p2

|�+i12 + |��i12

1p2

| +i12 + | �i12 =


|�±i =1p2(|0i|0i± |1i|1i)

| ±i =1p2(|0i|1i± |1i|0i)

Bell States:

=1p2

|�+i12 + |��i12

1p2

| +i12 + | �i12 =

=1p2

| +i12 � | �i12


|�±i =1p2(|0i|0i± |1i|1i)

| ±i =1p2(|0i|1i± |1i|0i)

Bell States:

=1p2

|�+i12 + |��i12

1p2

| +i12 + | �i12 =

=1p2

| +i12 � | �i12

1p2

|�+i12 � |��i12 =

Rewriting...

|�i123 = �12

| �i12(a|0i3 + b|1i3)�12

| +i12(a|0i3 � b|1i3)

+12

|�+i12(a|1i3 + b|0i3) +12

| +i12(a|1i3 � b|0i3)�� +

Rewriting...

|�i123 = �12

| �i12(a|0i3 + b|1i3)�12

| +i12(a|0i3 � b|1i3)

+12

|�+i12(a|1i3 + b|0i3) +12

| +i12(a|1i3 � b|0i3)

a|0i3 + b|1i3 = |⌘i3| �i12

| +i12

|�+i12

|��i12

Bell state measurement on qubits 1 and 2 qubit 3 is left in state

a|0i3 � b|1i3 = R1|⌘i3 Z

a|1i3 + b|0i3 = R2|⌘i3 X

a|1i3 � b|0i3 = R3|⌘i3 XZ

�� +

Rewriting...

|�i123 = �12

| �i12(a|0i3 + b|1i3)�12

| +i12(a|0i3 � b|1i3)

+12

|�+i12(a|1i3 + b|0i3) +12

| +i12(a|1i3 � b|0i3)

4 equiprobable results (2 bits) !A (12) sends 2 bits of information to B (3), B applies I, X, Z, or ZX to recover state η

a|0i3 + b|1i3 = |⌘i3| �i12

| +i12

|�+i12

|��i12

Bell state measurement on qubits 1 and 2 qubit 3 is left in state

a|0i3 � b|1i3 = R1|⌘i3 Z

a|1i3 + b|0i3 = R2|⌘i3 X

a|1i3 � b|0i3 = R3|⌘i3 XZ

�� +

QUANTUM TELEPORTATION

|0i

|0i

| i

H

H 0/1X Z

0/1

| i

classical wires


|0i

|0i

| i

H

H 0/1X Z

0/1

Entanglement Generation

| i

classical wires


|0i

|0i

| i

H

H 0/1X Z

0/1


Measurement in Bell basis

| i

classical wires


|0i

|0i

| i

H

H 0/1X Z

0/1


Measurement in Bell basis

Single-qubit correction

| i

classical wires

Efficient long-distance quantum tele-portation1 is crucial for quantum communication and quantum net-

working schemes2. Here we describe thehigh-fidelity teleportation of photons overa distance of 600 metres across the RiverDanube in Vienna, with the optimal effi-ciency that can be achieved using linearoptics. Our result is a step towards theimplementation of a quantum repeater3,which will enable pure entanglement to beshared between distant parties in a publicenvironment and eventually on a world-wide scale.

Quantum teleportation is based on a quantum channel, here establishedthrough a pair of polarization-entangledphotons shared between Alice and Bob(Fig. 1).We have implemented this by usingan 800-metre-long optical fibre installed ina public sewer system located in a tunnelunderneath the River Danube, where it isexposed to temperature fluctuations andother environmental factors.

For Alice to be able to transfer theunknown polarization state of an input pho-ton !"#b, she has to perform a joint Bell-statemeasurement on the input photon b and hermember, c, of the shared entangled photonpair (c and d). Our scheme allows her toidentify two of the four Bell states, the opti-mum achievable with only linear optics4,5.

As a result of this Bell-state measure-ment, Bob’s ‘receiver’ photon d will be pro-jected into a well defined state that alreadycontains full information on the originalinput photon b, except for a rotation thatdepends on the specific Bell state that Aliceobserved. Our teleportation scheme there-fore also includes active feed-forward ofAlice’s measurement results, which isachieved by means of a classical microwavechannel together with a fast electro-opticalmodulator (EOM). It enables Bob to per-form the unitary transformation on pho-ton d to obtain an exact replica of Alice’sinput photon b.

Specifically, if Alice observes the !$%#bc

Bell state, which is the same as the initialentangled state of photons c and d, thenBob already possesses the original inputstate. But if Alice observes the !$&#bc state,he introduces a '-phase shift between thehorizontal and vertical polarization com-ponents of photon d by applying a voltagepulse of 3.7 kV on the EOM. For successfuloperation, Bob has to set the EOM cor-rectly before photon d arrives. Because ofthe reduced velocity of light within thefibre-based quantum channel (two-thirdsof that in vacuo), the classical signal arrives

about 1.5 microseconds before the photon.We demonstrated the teleportation of

three distinct polarization states: linear at45°, left-handed circular or horizontal. Theteleportation fidelity achieved was 0.84,0.86 or 0.90 for the 45°, for each of theseinput states, respectively. These fidelitiescomfortably surpass the classical limit of0.66 (ref. 6) and prove that our teleporta-tion system is operating correctly. Withoutoperation of the EOM, however, Bobobserves a completely mixed polarizationfor the 45° and circular polarization inputstates, causing the observed fidelity forthese states to drop to 0.54 and 0.59, respec-tively, in the absence of active unitary trans-formation. The deviation from the randomfidelity of 0.5 is due to statistical fluctua-tions in the observed counts.

Each measurement run lasted for 28 hand the rate of successful teleportationevents was 0.04 per second. Polarizationstability proved to be better than 10° on thefibre between Alice’s and Bob’s labs, corre-sponding to an ideal teleportation fidelityof 0.97 over a full measurement run. Hence,despite the exposure of our system to theenvironment, high-fidelity teleportationwas still achievable without permanentreadjustments.

We have demonstrated quantum tele-portation over a long distance and withhigh fidelity under real-world conditions

brief communications

NATURE | VOL 430 | 19 AUGUST 2004 | www.nature.com/nature 849

outside a laboratory. Our system combinesfor the first time, to our knowledge, animproved Bell-state analyser with activeunitary transformation, enabling a doub-ling of the efficiency of teleportation compared with earlier experiments basedon independent photons7,8. Our experi-ment demonstrates feed-forward of mea-surement results, which will be essential forlinear-optics quantum computing9–11, andconstitutes a step towards the full-scaleimplementation of a quantum repeater.Rupert Ursin*, Thomas Jennewein*†,Markus Aspelmeyer*, Rainer Kaltenbaek*,Michael Lindenthal*, Philip Walther*,Anton Zeilinger*†*Institute for Experimental Physics, University ofVienna, 1090 Vienna, Austriae-mail: [email protected]†Austrian Academy of Science, 1090 Vienna, Austria1. Bennett, C. H. et al. Phys. Rev. Lett. 70, 1895–1899 (1993).

2. Bose, S., Vedral, V. & Knight, P. L. Phys. Rev. A 57, 822–829

(1998).

3. Briegel, H. J., Dür, W., Cirac, J. I. & Zoller, P. Phys Rev. Lett.

81, 5932–5935 (1998).

4. Lütkenhaus, N., Calsamiglia, J. & Suominen, K.-A. Phys. Rev. A

59, 3295–3300 (1999).

5. Kim, Y.-H. et al. Phys. Rev. Lett. 86, 1370–1373 (2001).

6. Popescu, S. Phys. Rev. Lett. 72, 797–799 (1994).

7. Bouwmeester, D. et al. Nature 390, 575–579 (1997).

8. Marcikic, I., de Riedmatten, H., Tittel, W., Zbinden, H. &

Gisin, N. Nature 421, 509–513 (2003).

9. Riebe, M. et al. Nature 429, 734–737 (2004).

10.Barrett, M. D. et al. Nature 429, 737–739 (2004).

11.Gottesmann, D. & Chuang, I. L. Nature 402, 390–393 (1999).

Competing financial interests: declared none.

Quantum teleportation across the DanubeA real-world experiment marks a step towards worldwide quantum communication.

Figure 1 Long-distance quantum teleportation across the River Danube. The quantum channel (fibre F) rests in a sewage-pipe tunnel

below the river in Vienna, while the classical microwave channel passes above it. A pulsed laser (wavelength, 394 nm; rate, 76 MHz) is

used to pump a (-barium borate (BBO) crystal that generates the entangled photon pair c and d and photons a and b (wavelength,

788 nm) by spontaneous parametric down-conversion. The state of photon b after passage through polarizer P is the teleportation input;

a serves as the trigger. Photons b and c are guided into a single-mode optical-fibre beam splitter (BS) connected to polarizing beam split-

ters (PBS) for Bell-state measurement. Polarization rotation in the fibres is corrected by polarization controllers (PC) before each run of

measurements. The logic electronics identify the Bell state as either !$%#bc or !$&#bc and convey the result through the microwave chan-

nel (RF unit) to Bob’s electro-optic modulator (EOM) to transform photon d into the input state of photon b.

19.8 Brief comms AM 12/8/04 4:57 pm Page 849

© 2004 Nature Publishing Group
















(1998).


81, 5932–5935 (1998).


59, 3295–3300 (1999).





Gisin, N. Nature 421, 509–513 (2003).
















2004
















(1998).


81, 5932–5935 (1998).


59, 3295–3300 (1999).





Gisin, N. Nature 421, 509–513 (2003).
















LETTERdoi:10.1038/nature11472

Quantum teleportation over 143 kilometres usingactive feed-forwardXiao-Song Ma1,2{, Thomas Herbst1,2, Thomas Scheidl1, Daqing Wang1, Sebastian Kropatschek1, William Naylor1,Bernhard Wittmann1,2, Alexandra Mech1,2, Johannes Kofler1,3, Elena Anisimova4, Vadim Makarov4, Thomas Jennewein1,4,Rupert Ursin1 & Anton Zeilinger1,2

The quantum internet1 is predicted to be the next-generationinformation processing platform, promising secure communica-tion2,3 and an exponential speed-up in distributed computation2,4.The distribution of single qubits over large distances via quantumteleportation5 is a key ingredient for realizing such a global plat-form. By using quantum teleportation, unknown quantum statescan be transferred over arbitrary distances to a party whose loca-tion is unknown. Since the first experimental demonstrations ofquantum teleportation of independent external qubits6, aninternal qubit7 and squeezed states8, researchers have progressivelyextended the communication distance. Usually this occurs withoutactive feed-forward of the classical Bell-state measurement result,which is an essential ingredient in future applications such as com-munication between quantum computers. The benchmark for aglobal quantum internet is quantum teleportation of independentqubits over a free-space link whose attenuation corresponds to thepath between a satellite and a ground station. Here we report suchan experiment, using active feed-forward in real time. The experi-ment uses two free-space optical links, quantum and classical, over143 kilometres between the two Canary Islands of La Palma andTenerife. To achieve this, we combine advanced techniques invol-ving a frequency-uncorrelated polarization-entangled photon pairsource, ultra-low-noise single-photon detectors and entanglement-assisted clock synchronization. The average teleported state fidelityis well beyond the classical limit9 of two-thirds. Furthermore,we confirm the quality of the quantum teleportation procedurewithout feed-forward by complete quantum process tomography.Our experiment verifies the maturity and applicability of suchtechnologies in real-world scenarios, in particular for futuresatellite-based quantum teleportation.

Significant progress has been made recently in the field of quantumcommunication based on optical free-space links10–19, which poten-tially allow much larger propagation distances compared to the exist-ing fibre networks because of the lower photon loss per kilometre. Toenable quantum communication on a global scale and among partiesnot having access to any fibre network, it is foreseeable that experi-ments will involve ground-to-satellite10,11,15 and inter-satellite links.

Previous experiments focused on the distribution of quantum statesof single photons or entangled photon pairs over optical free-spacelinks. However, the realization of more sophisticated multiphotonquantum information protocols, such as quantum teleportation,remained an experimental challenge under real-world conditions.Quantum teleportation is based on the simultaneous creation of atleast three photons, which for random photon pair sources reducesthe count rate by several orders of magnitude compared to experi-ments using only two photons16,19. This decreases the signal-to-noiseratio and requires a long integration time, such that high system

stability is necessary. Moreover, the complexity and environmentalrequirements of a quantum teleportation set-up are increased signifi-cantly compared to previous two-photon experiments, which providessignificant experimental and technological challenges. The work pre-sented in ref. 18 was a significant achievement in long-distancequantum communication, harnessing the entanglement between dif-ferent degrees of freedom of a single photon. However, because theteleported qubit was not provided independently from the outside, theapplicability of that scheme is limited. Most earlier experiments onteleportation of qubits and squeezed states6–8 were in-laboratorydemonstrations, and hence the communication distances were rathershort. Although fibre-based teleportation has been demonstratedexperimentally20,21, the maximum transmission distance is limited bythe intrinsic photon loss in optical fibre, unless quantum repeaters areinvolved22. In comparison to these previous studies, the experimentpresented in this Letter achieves long-distance free-space teleportationof an independent quantum state, thus paving the way for satellite-based global quantum communication.

Quantum teleportation relies on using both a quantum channel anda classical channel between two parties, usually called Alice and Bob5

(here located in La Palma and Tenerife respectively; Fig. 1a). Thequantum channel is used by Alice and Bob to share the entangledauxiliary state23

Y{j i23~1ffiffiffi2p Hj i2 Vj i3{ Vj i2 Hj i3" #

ð1Þ

which is one of the four maximally entangled Bell states( Y+$$ %

~ 1ffiffi2p Hj i Vj i+ Vj i Hj ið Þ and W+

$$ %~ 1ffiffi

2p Hj i Hj i+ Vj i Vj ið Þ).

jHæ and jVæ denote the horizontal and vertical polarization states. Aliceand Bob share this entangled state, where photon 2 is with Alice andphoton 3 is with Bob. Charlie provides the input photon 1 to be tele-ported to Alice in a general polarization state

wj i1~a Hj i1zb Vj i1 ð2Þwhere a and b are complex numbers (jaj2 1 jbj2 5 1), unknown toboth Alice and Bob.

Alice then performs a Bell-state measurement (BSM), projectingphotons 1 and 2 randomly onto one of the four Bell states each withthe same probability of 25%. As a consequence, photon 3 is projectedonto the input state jwæ, up to a unitary transformation (U), whichdepends on the outcome of the BSM. When Alice feeds the outcome ofthe BSM forward to Bob via the classical channel, he can implementthe corresponding unitary operation in real time and thus obtainphoton 3 in the initial state (equation (2)) of photon 1. If jY2æ12 isdetected, then U corresponds to the identity operation, which meansthat Bob needs to do nothing. If, on the other hand, jY1æ12 is detected,Bob has to apply a p phase shift between the horizontal and the verticalcomponent of his photon 3.

1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria. 2Vienna Center for Quantum Science and Technology, Facultyof Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria. 3Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching/Munich, Germany. 4Institute forQuantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada. {Present address: Department of ElectricalEngineering, Yale University, New Haven, Connecticut 06520, USA.

1 3 S E P T E M B E R 2 0 1 2 | V O L 4 8 9 | N A T U R E | 2 6 9

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Our experiment was conducted between Alice’s transmitter station(at the Jacobus Kapteyn Telescope (JKT) of the Isaac Newton Groupon La Palma) and Bob’s receiver station (at the Optical Ground Station(OGS) of the European Space Agency on Tenerife), separated by143 km, both at altitudes of about 2,400 m. Our experimental set-upis shown in Fig. 1b. At La Palma, near-infrared femtosecond pulses(with a central wavelength of 808 nm) emitted from a mode-lockedTi:sapphire laser, with a repetition rate of 80 MHz, were up-convertedto blue pulses (with a central wavelength of 404 nm). They were usedto generate two photon pairs via type-II spontaneous parametricdown conversion (SPDC) in two nonlinear b-barium borate (BBO)crystals placed in sequence. The first SPDC source was aligned toemit the entangled auxiliary photon pairs (photons 2 and 3) in thejY2æ23 state24, equation (1), while the second crystal was a heralded

single-photon (HSP) source providing Charlie’s photon 1 to be tele-ported. That source delivered pairs of horizontally (photon 0) andvertically (photon 1) polarized photons in a product state. The detec-tion of photon 0 by the avalanche photodiode (APD) t served as atrigger to herald the presence of photon 1. All photons were spectrallyfiltered using interference filters (IF) and coupled into single-modefibres for spectral and spatial mode selection.

To realize the BSM, Alice’s photon 2 was overlapped on a fibre beamsplitter (FBS) with the teleportation input photon 1, whose polariza-tion was arbitrarily prepared by Charlie using half- and quarter-waveplates (HWP and QWP). In each output port of the FBS, a polarizingbeam splitter (PBS) was used to project these photons on either hori-zontal or vertical polarization. Fibre polarization controllers (FPCs)were used to compensate for unwanted polarization rotation induced

Tx

Bob

2 31

BSM143 km

Classical feed-forward channel

0Quantum channel

EPR

N

143 km

Classical feed-forward channel

Quantum channel

Tracking

EPR/Alice

HSP/Charlie

t

808 nm

CCD 532 nm

100 m

1,064 nm

BSM/Alice

TTU/Logic

d

a

c

b

GPS

532 nm

TTU/Logic

GPS

c

Pump Beam paths

BBO

PBS MirrorHWP QWP IF 8 nm IF 3 nm Beam dump

Fibre

Coil

Coupler

FPC APDc

EOM

Cable DM

7 cm diam. lens

14 cm diam. lens

PD

Laser

FBS

Rx

404 nm fs pulsed 80 MHz

BBO1

BBO2

a

b

0

12

3

La Palma

I1

Ψ12– /Ψ12

+

Tenerife

I3

I/π

Ψ +

Ψ –

HSP

Ψ +

CC

D

f

e

Ψ− ⟩23%

Figure 1 | Quantum teleportation between the Canary Islands La Palma andTenerife over both quantum and classical 143-km free-space channels.a, Experimental scheme. Alice and Charlie are situated in La Palma, and Bob inTenerife. Charlie prepares the teleportation input photon 1 in | wæ1, using aheralded single-photon (HSP) source with a trigger photon 0 (photons areindicated by black numerals on red circles). An Einstein–Podolsky–Rosen(EPR)23 source generates an entangled pair of photons 2 and 3 in the state| Y2æ23. Alice then performs a Bell-state measurement (BSM) on photons 1 and2, and projects them onto two of the four Bell states ( | Y2æ12/ | Y1æ12), and sendsthe result via the classical feed-forward channel to Bob. Photon 3 is sent via thefree-space quantum channel to Bob, who applies a unitary transformation(identity operation or p phase shift) on photon 3 depending on the BSM resultand thus turns its state | wæ3 into a replica of the initial quantum state | wæ1.b, Set-up. In La Palma, a frequency-uncorrelated polarization-entangled

photon pair source generated photons 2 and 3 in BBO1 (EPR/Alice) and acollinear photon pair source generated photons 0 and 1 in BBO2 (HSP/Charlie).All single photons were coupled into single-mode fibres. For implementing theBSM, photons 1 and 2 interfered in a fibre beam splitter (FBS) followed bypolarization-resolving single-photon detection (BSM/Alice). Photon 3 wasguided to the transmitter telescope via a 100-m single-mode fibre and sent toBob in Tenerife, where the unitary transformation was implemented using anelectro-optical modulator (EOM) and photon 3’s polarization was measured. Areal-time feed-forward operation was implemented by encoding the | Y1æ12

BSM result in 1,064-nm laser pulses, which were then sent to Bob via the feed-forward channel. On Bob’s side, they were separated by a dichroic mirror (DM),detected with a photodetector (PD) and used to trigger the EOM to perform therequired p phase shift operation. See main text for details.

RESEARCH LETTER

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