R ESEARCH A RTICLES our experiment achieves Fexp ϭ 0.58 Ϯ 0.02 for the field emerging from Bob’s station, thus Unconditional Quantum demonstrating the nonclassical character of this experimental implementation. Teleportation To describe the infinite-dimensional states of optical fields, it is convenient to introduce a A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, pair (x, p) of continuous variables of the electric H. J. Kimble,* E. S. Polzik field, called the quadrature-phase amplitudes (QAs), that are analogous to the canonically Quantum teleportation of optical coherent states was demonstrated experi- conjugate variables of position and momentum mentally using squeezed-state entanglement. The quantum nature of the of a massive particle (15). In terms of this achieved teleportation was veriﬁed by the experimentally determined ﬁdelity analogy, the entangled beams shared by Alice Fexp ϭ 0.58 Ϯ 0.02, which describes the match between input and output states. and Bob have nonlocal correlations similar to A ﬁdelity greater than 0.5 is not possible for coherent states without the use those first described by Einstein et al.(16). The of entanglement. This is the ﬁrst realization of unconditional quantum tele- requisite EPR state is efficiently generated via portation where every state entering the device is actually teleported. the nonlinear optical process of parametric down-conversion previously demonstrated in Quantum teleportation is the disembodied subsystems of infinite-dimensional systems (17). The resulting state corresponds to a transport of an unknown quantum state from where the above advantages can be put to use. squeezed two-mode optical field. In the ideal one place to another (1). All protocols for Finally, a relatively simple design is imple- case, namely perfect EPR correlations and loss- accomplishing such transport require nonlo- mented that eliminates the need for some less propagation and detection, the teleported cal correlations, or entanglement, between nonlinear operations (10); these nonlinear op- state emerges from Bob’s station with perfect systems shared by the sender and receiver. erations constitute the main bottleneck to the fidelity F ϭ 1(10). John Bell’s famous theorem on the incompat- efficacy of other teleportation schemes. Apart from the advantages of continuous ibility of quantum mechanics with local hid- This teleportation scheme uses the proto- quantum variables, our experiment is sig- den variable theories establishes that entan- col described in (10). The experimental setup nificant in that it attains full teleportation as glement represents the quintessential distinc- (Fig. 1) consists of a sending station operated originally envisioned in (1). This is in con- tion between classical and quantum physics by Alice, a receiving station operated by Bob, trast to previous teleportation experiments (2). Recent advances in the burgeoning field and a station for producing beams of entan- where no physical state enters the device of quantum information have shown that en- gled photons [labeled EPR (Einstein-Podol- from the outside (7) or where the teleported tanglement is also a valuable resource that sky-Rosen) beams (1, 2)]. Alice and Bob state is destroyed at Bob’s station (8), never can be exploited to perform otherwise impos- each receive half of the EPR photons. Alice’s emerging for subsequent exploitation (18). sible tasks, of which quantum teleportation is station consists of two homodyne detectors Furthermore, in both these previous exper-

the prime example. Dx,p (including two local oscillators LOx,p), iments, there never exists an actual physi- Teleportation of continuous quantum where x and p denote the real and imaginary cal field with high (nonclassical) teleporta- variables. To date, most attention has fo- components of the (complex) electric field. tion fidelity at the output. cused on teleporting the states of finite-di- These detectors measure an entangled com- Apparatus and protocol. As illustrated ͉ ͘ mensional systems, such as the two polariza- bination of the input state vin and Alice’s in Fig. 1, entangled EPR beams are generated tions of a photon or the discrete level struc- half of the EPR beam. Classical lines of along paths {1, 2} by combining two inde- ture of an atom (1, 3–8). However, quantum communication are used to transmit Alice’s pendent squeezed beams at a 50/50 beam teleportation is also possible for continuous measurement results to Bob, who then uses splitter (19), with the relative phase between variables corresponding to states of infinite- that information to transform the second half the squeezed fields actively servo-controlled.

dimensional systems (9, 10), such as optical of the EPR beam (at the mirror mBob) into an The squeezed fields are themselves produced fields or the motion of massive particles (11). output ˆout that closely mimics the original by parametric down-conversion in a sub- The particular implementation of teleported unknown input. threshold optical parametric oscillator (OPO) optical fields is noteworthy in four ways. In our scheme, a third party, Victor (the (20). The particular setup is as described in First, the relevant optical tools are power- verifier), prepares an initial input in the form (21), save one important exception. Because ful and well suited for integration into of a coherent state of the electromagnetic the cavity for the OPO is a traveling-wave ͉ ͘ an evolving communication technology. Sec- field vin , which he then passes to Alice for resonator (that is, a folded-ring geometry), it ond, these methods apply to other quantum teleportation. Likewise, the teleported field is possible to drive the intracavity nonlinear computational protocols, such as quantum er- that emerges from Bob’s sending station is crystal with two counterpropagating pump ror correction for continuous variables using interrogated by Victor to verify that telepor- beams to generate two (nominally) indepen- linear optics (12) and superdense coding of tation has actually taken place: At this stage, dent squeezed fields countercirculating with- optical information (13). Third, finite-dimen- Victor records the amplitude and variance of in the cavity and emerging along the separate sional systems can always be considered as the field generated by Bob, and is thereby paths {i, ii} (see Fig. 1). Note that the light able to assess the “quality” of the teleporta- from a single-frequency titanium sapphire tion protocol. This is done by determining the (TiAl O ) laser at 860 nm serves as the pri- A. Furusawa, C. A. Fuchs, H. J. Kimble are in the 2 3 Norman Bridge Laboratory of Physics, California In- overlap between input and output as given by mary source for all fields in our experiment. ϵ͗ ͉ ͉ ͘ stitute of Technology, Pasadena, CA 91125, USA. J. L. the fidelity F vin ˆout vin . As discussed Ninety percent of the laser output at frequen- Sørensen and E. S. Polzik are at the Institute of Physics below, for the teleportation of coherent states, cy L is directed to a frequency-doubling and Astronomy, Aarhus University, Aarhus 8000, Den- ϭ Fc 0.5 sets a boundary for entrance into the cavity to generate roughly 300 mW of blue mark. S. L. Braunstein is at the School of Electrical Engineering and Computer Systems, University of quantum domain in the sense that Alice and light at 2 L (22), with this output then split Wales, Bangor LL57 1UT, UK. Bob can exceed this value only by making use into two beams that serve as harmonic pumps *To whom correspondence should be addressed. E- of entanglement (14). From Victor’s measure- for (degenerate) parametric down-conver- 3 Ϯ⍀ mail: [email protected] ments of orthogonal quadratures (see below), sion, 2 L L , within the OPO. Both

706 23 OCTOBER 1998 VOL 282 SCIENCE www.sciencemag.org R ESEARCH A RTICLES the doubling cavity and the cavity of the OPO ϩ ͑ Ϫ 2͒ ϩ 2͑ 2͒ Ϫ coherent state only by way of shared quantum 1 2 2g 1/ 1) (2) contain an a-cut potassium niobate (KNbO3) entanglement, as can be operationally (and crystal for temperature-tuned, noncritical phase Here, Ϯ are the variances of the amplified/ independently) verified by Victor (14). Note matching, with the lengths of both cavities squeezed QAs that are summed to form the that for experiments involving photon polar- Ϯ ϭϮ under servo-control to maintain resonance for EPR beams (assuming i ii ), 1,2 char- ization as in (7, 8), the corresponding fidelity a TEM00 longitudinal mode. acterize the (amplitude) efficiency with threshold for a completely unknown quantum Our protocol is as follows: EPR beam 1 which the EPR beams are propagated and state is F Ͼ 2/3 (28), which could not be (Fig. 1) propagates to Alice’s sending station, detected along paths {1, 2}, and gives the approached because of the low detection ef- where it is combined at a 50/50 beam splitter (amplitude) efficiency for detection of the ficiencies. Moreover, in contrast to the work ͉ ͘ with the unknown input state vin , which is a unknown input state by Alice (10). in (7, 8), Victor need not to make any ar- ϵ coherent state of complex amplitude vin xin Classical teleportation replaces the EPR rangement with Alice and Bob in order to ϩ Ϯ ipin. Alice uses two sets of balanced homo- beams by (uncorrelated) vacuum inputs ( make an objective assessment of the quantum 3 dyne detectors (Dx,Dp) to make a “Bell-state” 1), thus eliminating the shared entangle- nature of the teleportation process. ϭ measurement of the amplitudes x (xin – x1)/ ment between Alice and Bob. For coherent Experimental results. We concentrate ͌ ϭ ϩ ͌ 2 and p (pin p1)/ 2 for the input state states distributed across the complex plane, first on Alice’s measurement of the unknown ␣ ϵ ϩ Ϸ and the EPR field 1 of amplitude 1 x1 ip1. optimum fidelity is achieved for g 1, in input state (Fig. 2). The spectral density of ϭ Ն Յ ⌿Alice ⍀ The classical (photocurrent) outcomes are de- which case ( Q –1) W 3 and F 0.5, photocurrent fluctuations x ( ), recorded ϭ noted by (ix, ip) respectively, and are scaled to and equality is obtained only for 1. In by Alice’s balanced homodyne detector Dx as (x, p). At unit efficiency, such detectors provide this case, one unit of vacuum noise in the the phase in of the coherent-state input [vin ϭ “optimal” information about (x, p) via (ix, ip) variance W of the Wigner distribution arises vin exp(i in)] is swept linearly by Victor, ϭ ϭ (23–25), with the knowledge gained about the from the original coherent-state input ( in is shown in Fig. 2A. For in – A,x p ͉ ͘ Ϫ unknown input state vin going to zero as i,ii 1), whereas the other two units are the so- (with integral p and A,x as the phase of local 3 Ϫ ⌿Alice ⍀ 0, where i,ii denotes the variances of called quantum duties (or quduties) that must oscillator at Dx), x ( ) rises to a maxi- squeezed QAs of the fields along paths {i, ii}. be paid at each crossing of the border be- mum, while for half-integral p it falls to a Because of the entanglement between the tween quantum and classical domains (10). minimum that is set by the variance of EPR EPR beams {1, 2}, Alice’s Bell-state detec- One quduty arises from Alice’s attempt to beam 1. A completely analogous set of traces tion collapses Bob’s field 2 into a state con- infer both QAs of the field (23); the other is obtained for the output from Alice’s detec- ditioned on the measurement outcome (ix, ip). quduty results from Bob’s displacement. tor Dp, except now shifted in phase by /2 in Hence, after receiving this classical informa- However, quantum teleportation should correspondence to the fact that phases of the

tion from Alice, Bob is able to construct the necessarily require Alice and Bob to share a local oscillator beams at (Dx,Dp) are fixed to teleported state ˆout via a simple phase-space nonlocal quantum resource, such as the EPR be in quadrature by active servo-control. For ϭ displacement of the EPR field 2 (26). In our beams in our experiment. The question of the vin 0, the phase-insensitive noise levels experiment, the amplitude and phase modu- operational verification of this shared entan- shown in Fig. 2A correspond to the case of no Ϯ 3 lators (Mx,Mp) shown in Fig. 1 transform the glement is relevant not only to our teleporta- EPR beams present [that is, i,ii 1, giving ⌽Alice ⍀ (amplified) photocurrents (ix, ip) into a com- tion protocol, but also to eavesdropping in the vacuum-state level 0,x ( )] and to that plex field amplitude, which is then combined quantum cryptography (27). So long as Alice with the EPR beam 1 distributed to Alice ⌳Alice ⍀ with the EPR beam 2 at the mirror mBob of and Bob can communicate only over a clas- [excess noise at the level x ( )]. A more reflectivity 0.99. In this manner, we affect the sical channel, we have shown that for g ϭ 1, detailed view of these noise levels is provided ␣ 3 ϭ␣ ϩ ͌ ϩ Ͼ ϩ c ϭ displacement 2 vout 2 g 2(ix iip) W in 2, so that W 3 heralds the in Fig. 2B. The observed increases in pho- ϭ ϩ ϩ ϩ ⌽Alice 3 ⌳Alice gvin [(x2 – gx1) i(p2 gp1)], where boundary between quantum and classical tocurrent fluctuations from 0,(x,p) (x,p) g describes Bob’s (suitably normalized) gain teleportation for coherent-state inputs. More represent the necessary degradation in signal- for the transformation from photocurrent to generally, even in the absence of loss, Alice to-noise ratio for Alice that accompanies Ϫ 3 Ͼ ⌳Alice 3 ϱ output field. In the limit i,ii 0, (x1 – x2, p1 and Bob can achieve F 1/2 for an unknown quantum teleportation, with (x,p) in the ϩ 3 p2) 0 [that is, the EPR beams become “quantum copies” of each other with respect ϭ 3 Fig. 1. Schematic of ix to their QAs (19)], so that for g 1, ˆout ͉ ͗͘ ͉ the experimental ap- Classical information vin vin , resulting in perfect teleportation 3 paratus for teleporta- ip with fidelity F 1. tion of an unknown Alice Quantum versus classical teleportation. ͉ ͘ quantum state vin Ð Ð Of course, the limit F ϭ 1 is reached only for from Alice’s sending D D Mx ideal (singular) EPR correlations and for loss- station to Bob’s re- x p ceiving terminal by less propagation and detection. To aid in M way of the classical in- p quantifying the “quality” of teleportation in Bob formation (ix, ip) sent our actual experiment, we calculate F for the LOx LOp from Alice to Bob mBob case of a finite degree of EPR correlation and and the shared entan- in the presence of non-unit efficiencies, glement of the EPR EPR Out which for a coherent-state input ͉v ͘ becomes beams (1, 2). In in 12beams F ϭ 2/ exp[Ϫ2͉v ͉2(1Ϫg)2/ ] (2) ρ

Q in Q out |v 〈 LOV in (14), where Q is the variance of the Q function of the teleported field, given by Victor DV iii Ð ϭ 1 ϩ g2 ϩ (Ϫ/2) (g ϩ)2 Q 1 2 OPO ϩ ͑ϩ ͒͑ Ϫ ͒2 ϩ ͑ Ϫ 2͒ 2 Pump 1 Pump 2 Victor /2 g 1 2 1 1 g

www.sciencemag.org SCIENCE VOL 282 23 OCTOBER 1998 707 R ESEARCH A RTICLES – limit of perfect teleportation (for which i,ii about the carrier L (that is, AM and FM relative to Alice’s and Bob’s fields, but it can as 3 ϩ 3 ϱ 0, i,ii , and hence the variance 1 of modulation sidebands), with FM sidebands well be freely scanned. As in Fig. 2, the phase- ⍀ the EPR beam 1 diverges). applied by Victor to create the input vin( ). insensitive noise levels in Fig. 3A correspond to ⍀ ⍀ ϭ The various spectral densities displayed in Given Alice’s measurement of (x( ), p( )), the case of a vacuum-state input vin 0, first Fig. 2 are directly related to the means and the next step in the protocol is for her to send with no EPR beams present (that is, classical ⍀ ⍀ Ϯ 3 ⌼ variances of the quadrature-phase amplitudes the (classical) photocurrents (ix( ), ip( )) to teleportation with i,ii 1), giving the level Victor ⍀ of the incident fields (17, 19). Because we are Bob, who uses this information to generate a 0 ( ), and then to quantum teleportation dealing with broad-bandwidth fields, the sin- displacement (a coherent modulation at ⍀)of with the EPR beams {1, 2} distributed to Alice gle-mode treatment of (10) must be general- the field in beam 2 by way of the modulators and Bob, giving ⌳Victor(⍀). These noise levels

ized to the case of multimode fields of finite (Mx,Mp) and the mirror mBob. Note that the are shown in somewhat more detail in Fig. 3B. bandwidth (29). In this situation, the relevant phases of both Alice’s and Bob’s fields relative For g ϭ 1 (0 dB), as here, the level ⍀ ⌼Victor ϳ quantities are the spectral components (x( ), to the EPR beams {1, 2} are fixed by servo- 0 stands 4.8 dB above Victor’s vacuum- ⍀ ⌽Victor p( )) of the QAs, where a general QA at control. Bob’s action results in the teleported state level 0 , in correspondence to the phase ␦ is defined by output field, which is subsequently interrogated three units of vacuum noise previously dis- by Victor by way of his own (independent) cussed. However, in contradistinction to the ⍀ ϩ ⌬⍀ balanced homodyne detector. Shown in Fig. 3 increases ⌽Alice 3 ⌳Alice recorded by Alice, z͑⍀,␦͒ § ͵ d⍀Ј͓aˆ ͑⍀Ј͒ exp(Ϫi␦͒ 0,(x,p) (x,p) is Victor’s measurement of the QAs of the Victor observes a decrease in fluctuations ⍀ Ϫ ⌬⍀ ⌼Victor 3 ⌳Victor teleported field, as expressed by the spectral 0 brought about by the presence ⌿Victor ⍀ ϩ aˆ †͑Ϫ⍀Ј͒ exp(ϩi␦)] (3) density of photocurrent fluctuations ( ) of the EPR beams, indicating the success of the as a function of time, again as the phase in is teleportation protocol. More quantitatively, for with aˆ(aˆ†) as the annihilation (creation) op- linearly swept. Here, the gain is g ϭ 1 (that is, g ϭ 1, Victor observes a decrease of 10[log ⍀ ⌳Victor ⍀ ⌼Victor ⍀ ϭ Ϯ erator for the field at offset from the optical 0 dB), so that Victor’s signal level rises 3 dB ( ) – log 0 ( )] –1.2 0.2 dB. ⍀ ⍀ ϭ ⍀ ⍀ ⌳Victor ⍀ ⌽Victor ⍀ carrier, with (x( ), p( )) (z( , 0), z( , above that in Fig. 2A, in correspondence to a The ratio ( )/ 0 ( ) then leads di- ⍀ ϭ Ϯ Ͻc /2)), and with the integration extending over reconstruction of the coherent amplitude vin( ) rectly to the variance W 2.23 0.03 W ⌬⍀ ⍀ 3 ⍀ ϭ a small interval about . We then have vout( ) for the output field. This transforma- 3 for the teleported field. tion is independent of the phase of the input Demonstration of quantum teleportation. ⌿͑⍀͒⌬⍀ ϳ ͗z2͑⍀,␦͒͘ (4) field relative to Alice’s detectors (Dx,Dp) and By carrying out a series of measurements sim- (15, 17). As shown in (29), the teleportation to the consequent division of this amplitude to ilar to those shown in Figs. 2 and 3, we have

protocol of (10) remains unchanged in its Bob’s modulators (Mx,Mp), so that the phase of explored the dependence of both the variance of essential character. However, now the state the teleported field tracks that of the input. In the teleported field and the fidelity F on Bob’s being teleported describes the field at fre- the particular case of Fig. 3A, the phase Victor gain g. Plotted in Fig. 4 as a function of g are Ϯ⍀ ⌬⍀ x,p quency offset within a bandwidth of Victor’s local oscillator is servo-controlled the variances W obtained by Victor at DV for

⌿Alice ⍀ Fig. 2 (left). (A) Spectral density of photocurrent ﬂuctuations x ( ) recorded by Alice’s balanced homodyne detector Dx as a function of time with the phase of the coherent-state input linearly swept. For the in ϭ case of a vacuum-state input vin 0 and with no EPR beams present, as afunction of time with the phase in of the coherent-state input ⌽Alice ⍀ ϭ Ϸ the vacuum-state level 0,x ( ) results, whereas with vin 0 and linearly swept and with the gain g 1. For the case of a vacuum-state ⌳Alice ⍀ ϭ EPR beam 1 distributed to Alice, excess noise at the level x ( )is input vin 0 and with no EPR beams present, the excess noise level ϭ ⌼Victor ⍀ ϭ recorded. (B) Expanded view for vin 0, now with a 10-trace average. 0 ( ) results, whereas with vin 0 and EPR beams {1, 2} Acquisition parameters: radio frequency (rf) ⍀/2ϭ2.9 MHz, rf distributed to Alice and Bob, the level of ﬂuctuations is reduced to bandwidth ⌬⍀/2ϭ30 kHz, video bandwidth ϭ 1 kHz (A) and 30 Hz ⌳Victor(⍀). The vacuum-state level for D is given by ⌽Victor.(B) ϭ V 0 (B). Fig. 3 (right). (A) Spectral density of photocurrent ﬂuctua- Expanded view for vin 0, now with a 10-trace average. Acquisition ⌿Victor ⍀ tions ( ) recorded by Victor’s balanced homodyne detector DV parameters are as in Fig. 2.

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x,p Fig. 4 (left). Variance W of the teleported ﬁeld measured by Victor as a function of the gain g used by Bob for the phase-space displacement of the EPR beam 2. Shown are data obtained both F with the quantum-correlated

EPR beams present (blue) and (dB) x,p W σ with vacuum-state inputs (red) Fidelity for beams {1, 2}. Open and ﬁlled symbols represent results of two different experiments. The theo- retical results from Eq. 2 (curves) are also shown for the two cases of quantum and classical tele- 2 portation. Fig. 5 (right). Fi- Gain g2 (dB) Gain g (dB) delity F inferred from measure- x,p ments of the input amplitude vin and of the quantities vout and Q for the teleported output ﬁeld. Data for the cases of classical (red) and quantum (blue) teleportation are shown, as are the theoretical results from Eq. 1 (curves). See text for explanations of ﬁlled and open symbols. F Ͼ 0.5 demonstrates the nonclassical nature of the protocol.

exp ϭ Ϯ Ͻ measurements with the phase Victor locked to be F c 0.48 0.03 Fc, and (ii) the 9. L. Vaidman, Phys. Rev. A 49, 1473 (1994). exp ϭ 10. S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, that of Alice’s local oscillator at detector Dx fidelity for quantum teleportation is Fq (squares) and D (triangles), with the open and 0.58 Ϯ 0.02 Ͼ F . Recall that F ϭ 0.5 is 869 (1998). p c c 11. B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, filled symbols from two different experiments. the classical bound attainable by Alice and 4033 (1986). Comparison of the data in Fig. 4 with the Bob in the absence of shared entanglement 12. S. L. Braunstein, Nature 394, 47 (1998). exp Ͼ 13. and H. J. Kimble, in preparation. theoretical result from Eq. 2 and the indepen- (14), so that Fq Fc demonstrates the dently measured quantities ϭ 0.90 Ϯ 0.04, nonclassical nature of the experiment. 14. S. L. Braunstein, C. A. Fuchs, H. J. Kimble, in 1,2 preparation. 2 ϭ Ϯ – ϭ Ϯ ϩ ϭ 0.97 0.02, and { 0.5 0.1, By exploiting squeezed-state entanglement, 15. M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 1.8 Ϯ 0.2} yields reasonable agreement. In we have the first realization of quantum tele- 2731 (1988); M. D. Reid, Phys. Rev. A 40, 913 (1989). particular, the EPR beams bring a reduction of portation as originally proposed in (1): An un- 16. A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 x,p below the limit c for classical teleporta- known quantum state input to Alice’s station is (1935). W W 17. Z. Y. Ou, S. F. Pereira, H. J. Kimble, K. C. Peng, Phys. tion with vacuum-state inputs over a reasonably transported to a field recreated at Bob’s remote Rev. Lett. 68, 3663(1992); Z. Y. Ou, S. F. Pereira, H. J. wide range in g. Results similar to these are station. The quantum nature of the protocol is Kimble, Appl. Phys. B 55, 265 (1992). 18. S. L. Braunstein and H. J. Kimble, Nature 394, 840 obtained for W with Victor swept independent demonstrated with reference to both the vari- of (D ,D ). Note that in a given experiment, we ance of the teleported field and its fidelity F (1998). x p W 19. H. J. Kimble, in Fundamental Systems in Quantum p x Ϸ observe a systematic increase in W / W relative to the original input state, where we Optics, Les Houches, Session LIII, 1990, J. Dalibard, J. M. Raimond, J. Zinn-Justin, Eds. (Elsevier, Amster- 1.05, which is presumably associated with emphasize that W and F relate to a physical asymmetries and non-ideal couplings of the field emerging from Bob’s station. Because we dam, 1992), pp. 549–674. 20. L. A. Wu et al., Phys. Rev. Lett. 57, 2520 (1986). squeezed beams {i, ii} that are summed to have made no correction for the finite efficien- 21. E. S. Polzik, J. Carri, H. J. Kimble, ibid. 68, 3020 (1992); produce the EPR beams {1, 2} (17). cy of Victor’s detection process, the fidelity of Appl. Phys. B 55, 279 (1992). Data as in Fig. 4, together with a record of the actual teleported field is higher than that 22. E. S. Polzik and H. J. Kimble, Opt. Lett. 16, 1400  ⍀ ϭ (1991). the mean coherent amplitude out( ) quoted. Even without such correction, the over- ⍀ 23. E. Arthurs and J. L. Kelly Jr., Bell. Syst. Tech. J. (April), gvin( ) measured by Victor for the teleported all efficiency of our scheme, together with the 725 (1965). field, allow us to infer the fidelity by way of shared entanglement of the EPR beams, ensure 24. H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory a simple generalization of Eq. 1, namely full quantum teleportation: A quantum state IT-26, 78 (1980). presented at the input is teleported with non- 25. S. L. Braunstein, Phys. Rev. A 42, 474 (1990). 2 classical fidelity on each and every trial (of 26. Related work involves feedforward manipulation of F ϭ exp͑Ϫ2͉v Ϫ v ͉2րͱx p ͒ (5) twin-beam states [P. R. Tapster, J. G. Rarity, J. S. ͱx p out in Q Q duration given by the inverse bandwidth 1/⌬⍀). Satchell, Phys. Rev. A 37, 2963 (1988); J. C. Mertz et Q Q This high-efficiency experimental implementa- al., Phys. Rev. Lett. 64, 2897 (1990)]. Here, x,p ϵ (1 ϩx,p) are the variances for the tion of a quantum algorithm for continuous 27. C. A. Fuchs and A. Peres, Phys. Rev. A 53, 2038 Q W (1996). Q function obtained by Victor from measure- variables suggests that other protocols, includ- 28. H. Barnum, thesis, University of New Mexico (1998). ments of the spectral densities of photocurrent ing quantum error correction (12) and super- 29. P. van Loock, S. L. Braunstein, H. J. Kimble, in fluctuations (that is, without correction for his dense coding (13) of optical fields, are not far preparation. detection efficiencies). Again under the as- from realization. 30. The experiment was carried out in the Quantum Optics Group at the California Institute of Technol- sumption of Gaussian statistics for the tele- ogy. Supported by the Quantum Information and ported field, we thus deduce F, with the results Computation Institute funded by the Defense Ad- shown in Fig. 5. The filled points around g ϭ 1 References and Notes vanced Research Projects Agency via the Army Re- 1. C. H. Bennett et al., Phys. Rev. Lett. 70, 1895 (1993). search Ofﬁce, by the Ofﬁce of Naval Research, and by (0 dB) are from independent measurements of 2. J. S. Bell, Speakable and Unspeakable in Quantum NSF. A.F. is a visiting scientist from the Nikon Re- x,p W , whereas for the open symbols, we approx- Mechanics (Cambridge Univ. Press, New York, 1988), search Laboratories. S.L.B. was funded in part by imate p Ϸ 1.05x , as above. The theoretical p. 196. Engineering and Physical Sciences Research Council W W 3. L. Davidovich et al., Phys. Rev. A 50, R895 (1994). (UK) grant GR/L91344. C.A.F. also acknowledges sup- curve is from Eq. 1 with the aforementioned port from a Lee A. DuBridge Fellowship. J.L.S. and Ϯ 4. J. I. Cirac and A. S. Parkins, ibid., p. R4441. values 1,2, , and . Although the agree- 5. T. Sleator and H. Weinfurter, Ann. N.Y. Acad. Sci. E.S.P. acknowledge support from the Danish Research ment between theory and experiment is 755, 715 (1995). Council. We gratefully acknowledge the contribu- evidently quite reasonable, the essential ob- 6. S. L. Braunstein and A. Mann, Phys. Rev. A 51, R1727 tions of N. Ph. Georgiades and discussions with C. M. (1995); ibid. 53, 630 (1996). Caves, N. Cohen, S. J. van Enk, and H. Mabuchi. servations are that (i) the fidelity for clas- 7. D. Boschi et al., Phys. Rev. Lett. 80, 1121 (1998). Ϯ ϭ sical teleportation with i,ii 1 is found to 8. D. Bouwmeester et al., Nature 390, 575 (1997). 20 July 1998; accepted 2 September 1998

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