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well-measured profiles3, suggesting that the absorbing gas has anear-primordial composition as expected for intergalactic gas.

Our models provide direct evidence that two characteristicproperties of quasars at low redshift are also applicable to brightquasars in the early Universe. These properties include the quasarspectral template, which determines the ionizing intensity of thequasar, and the relation between black hole mass and halo velocitydispersion, which we have used to determine the host halo mass.Both observed spectra show a blue peak of about 75% of the heightof the red (positive velocity) peak, and this is roughly matched bythe models. However, if we were to increase the ionizing intensity byan order of magnitude, then we would predict a blue peak at least ofequal height to the other peak. If, instead, we decreased the ionizingintensity by an order of magnitude, then the resulting blue peakwould be under 50% of the height of the red peak and thetransmitted flux would decrease to zero toward negative velocitiesmuch faster than is observed. Similarly, if we varied the assumedhalo mass by more than an order of magnitude then the resultingabsorption profile in each quasar would disagree with the data.High-redshift quasars could in principle be much fainter intrinsi-cally than they appear, if they are magnified by gravitationallensing16; our limits on the ionizing intensity, however, suggestthat the two quasars we have modelled cannot be magnified by afactor of more than about ten.

We can also estimate from the data the total gas infall rates intothese massive galaxies. The positions of the accretion shocks imply,in our models, infall velocities of 400–550 km s21 and shock radii of80–90 kpc. Gas at this radius is expected to have a density of about20 times the cosmic mean density5, so we obtain accretion rates of1,300 M( yr21 (z ¼ 4.795) and 2,900 M ( yr21 (z ¼ 6.28), respect-ively. At these rates, the host galaxies of these two quasars could havebeen assembled in (2–3) £ 108 yr, consistent with the 9 £ 108 yr ageof the Universe at z ¼ 6.28. Future comparison of our model to theaverage Lya absorption profile of a statistical sample of bright, earlyquasars with similar luminosities and redshifts should allow us to fitthe details of the absorption spectrum and refine our quantitativeconclusions. A

Received 25 September; accepted 26 November 2002; doi:10.1038/nature01330.

1. Fan, X. et al. Survey of z . 5.8 quasars in the Sloan digital sky survey. I. Discovery of three new quasars

and the spatial density of luminous quasars at z , 6. Astron. J. 122, 2833–2849 (2001).

2. Barkana, R. & Loeb, A. In the beginning: the first sources of light and the reionization of the universe.

Phys. Rep. 349, 125–238 (2001).

3. Zheng, W. et al. Five high-redshift quasars discovered in commissioning imaging data of the Sloan

Digital Sky Survey. Astron. J. 120, 1607–1611 (2000).

4. Becker, R. H. et al. Evidence for reionization at z , 6: Detection of a Gunn-Peterson trough in a

z ¼ 6.28 quasar. Astron. J. 122, 2850–2857 (2001).

5. Loeb, A. & Eisenstein, D. J. Probing early clustering with Lya absorption lines beyond the quasar

redshift. Astrophys. J. 448, 17–26 (1995).

6. Ferrarese, L. & Merritt, D. A fundamental relation between supermassive black holes and their host

galaxies. Astrophys. J. 539, L9–L12 (2000).

7. Tremaine, S. et al. The slope of the black hole mass versus velocity dispersion correlation. Astrophys. J.

574, 740–753 (2002).

8. Wyithe, J. S. B., Loeb, A. A physical model for the luminosity function of high-redshift quasars.

Astrophys. J. (in the press).

9. Vanden Berk, D. E. et al. Composite quasar spectra from the Sloan Digital Sky Survey. Astron. J. 122,

549–564 (2001).

10. Telfer, R. C., Zheng, W., Kriss, G. A. & Davidsen, A. F. The rest-frame extreme-ultraviolet spectral

properties of quasi-stellar objects. Astrophys. J. 565, 773–785 (2002).

11. Yuan, W., Brinkmann, W., Siebert, J. & Voges, W. Broad band energy distribution of ROSAT detected

quasars. II. Radio-quiet objects. Astron. Astrophys. 330, 108–122 (1998).

12. Abel, T. & Haehnelt, M. G. Radiative transfer effects during photoheating of the intergalactic medium.

Astrophys. J. 520, L13–L16 (1999).

13. Fan, X. et al. Evolution of the ionizing background and the epoch of reionization from the spectra of

z , 6 quasars. Astron. J. 123, 1247–1257 (2002).

14. Barkana, R. Did the universe reionize at redshift six? New Astron. 7, 85–100 (2002).

15. Miralda-Escude, J. Reionization of the intergalactic medium and the damping wing of the Gunn-

Peterson trough. Astrophys. J. 501, 15–22 (1998).

16. Wyithe, J. S. B. & Loeb, A. Magnification of light from many distant quasars by gravitational lenses.

Nature 417, 923–925 (2002).

17. Gunn, J. E. & Gott, J. R. On the infall of matter into clusters of galaxies and some effects on their

evolution. Astrophys. J. 176, 1–19 (1972).

18. Bertschinger, E. Self-similar secondary infall and accretion in an Einstein–de Sitter universe.

Astrophys. J. Suppl. 58, 39–65 (1985).

19. Keshet, U., Waxman, E., Loeb, A., Springel, V., Hernquist, L. Gamma-rays from intergalactic shocks.

Astrophys. J. (in the press).

20. Abel, T., Bryan, G. L. & Norman, M. L. The formation of the first star in the universe. Science 295,

93–98 (2002).

21. Scharf, C. A., Mukherjee, R. A statistical detection of gamma-ray emission from galaxy clusters:

implications for the gamma-ray background and structure formation. Astrophys. J. 580, 154–163

(2002).

22. Loeb, A. & Waxman, E. Cosmic g-ray background from structure formation in the intergalactic

medium. Nature 405, 156–158 (2000).

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142, 1633–1641 (1965).

24. Bajtlik, S., Duncan, R. C. & Ostriker, J. P. Quasar ionization of Lya clouds—the proximity effect, a

probe of the ultraviolet background at high redshift. Astrophys. J. 327, 570–583 (1988).

25. Haiman, Z. The detectability of high-redshift Lya emission lines prior to the reionization of the

universe. Astrophys. J. 576, L1–L4 (2002).

26. Miralda-Escude, J., Haehnelt, M. & Rees, M. J. Reionization of the inhomogeneous universe.

Astrophys. J. 530, 1–16 (2000).

27. Loeb, A. & Rybicki, G. B. Scattered Lyman alpha radiation around sources before cosmological

reionization. Astrophys. J. 524, 527–535 (1999).

28. Haiman, Z. & Rees, M. J. Extended Lyman alpha emission around young quasars: A constraint on

galaxy formation. Astrophys. J. 556, 87–92 (2001).

29. Pentericci, L. et al. VLT optical and near-infrared observations of the z ¼ 6.28 quasar SDSS

J1030 þ 0524. Astron. J. 123, 2151–2158 (2002).

30. Brotherton, M. S., Wills, B. J., Steidel, C. C. & Sargent, W. L. W. Statistics of QSO broad emission-line

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Acknowledgements We thank E. Turner and H. Netzer for discussions, and are grateful for the

hospitality of the Institute for Advanced Study where this work was completed. R.B. acknowledges

the support of an Alon Fellowship at Tel Aviv University and of the Israel Science Foundation. A.L.

acknowledges support from the Institute for Advanced Study and a John Simon Guggenheim

Memorial Fellowship. This work was also supported by the National Science Foundation.

Competing interests statement The authors declare that they have no competing financial

interests.

Correspondence and requests for materials should be addressed to R.B.

(e-mail: barkana@wise.tau.ac.il) or A.L. (e-mail: loeb@ias.edu).

..............................................................

Experimental extraction of anentangled photon pair fromtwo identically decohered pairsTakashi Yamamoto*†, Masato Koashi*†, Sahin Kaya Ozdemir*†& Nobuyuki Imoto*†‡

* School of Advanced Sciences, The Graduate University for Advanced Studies(SOKENDAI), Hayama, Kanagawa, 240-0193, Japan† CREST Interacting Carrier Electronics Project, 4-1-8 Honmachi, Kawaguchi,331-0012, Japan‡ NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, 243-0198, Japan.............................................................................................................................................................................

Entanglement is considered to be one of the most importantresources in quantum information processing schemes, includ-ing teleportation1–3, dense coding4 and entanglement-basedquantum key distribution5. Because entanglement cannot begenerated by classical communication between distant parties,distribution of entangled particles between them is necessary.During the distribution process, entanglement between theparticles is degraded by the decoherence and dissipation pro-cesses that result from unavoidable coupling with the environ-ment. Entanglement distillation and concentration schemes6–9

are therefore needed to extract pairs with a higher degree ofentanglement from these less-entangled pairs; this is accom-plished using local operations and classical communication.Here we report an experimental demonstration of extractionof a polarization-entangled photon pair from two decohered

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photon pairs. Two polarization-entangled photon pairs are gen-erated by spontaneous parametric down-conversion and thendistributed through a channel that induces identical phasefluctuations to both pairs; this ensures that no entanglement isavailable as long as each pair is manipulated individually. Then,through collective local operations and classical communicationwe extract from the two decohered pairs a photon pair that isobserved to be polarization-entangled.

Several experimentally feasible schemes have been proposed forthe extraction of photon pairs with a higher degree of entanglementfrom less-entangled pairs10–13 using local operations and classicalcommunication (LOCC). Kwiat et al.14 have recently demonstratedthat this is experimentally possible by local filtering. The localfiltering is essentially an operation individually applied to eachdistributed pair: each pair goes through the filtering process andsome of the pairs are discarded, while the surviving pairs havehigher entanglement. The next step is to realize LOCC operationsthat are collectively applied to several pairs. The collective opera-tions provide entanglement distillation and concentration for abroader class of noisy channels and with higher efficiency6–9.Recently, we have proposed a feasible concentration scheme12

based on a collective operation on two pairs with linear opticsand photon detectors. In the following we will first briefly introducethis scheme and then describe the experimental realization.

Suppose that Alice and Bob want to share photon pairs inmaximally entangled states:

jFð^Þl62 ;1ffiffiffi2p ðjHl6jHl2 ^ jVl6jVl2Þ ð1Þ

where jH l and jV l represent horizontal and vertical polarizationstates, respectively. The subscript numbers represent the locationof the photons in Fig. 1. Note that the states jF (þ)l62 and jF (2)l62

can be easily converted to each other locally. Bob first prepares amaximally entangled photon pair in jF (þ)l12, and sends its half toAlice through a quantum channel. This channel adds a phase shift fthat is fluctuating and hence is unknown. Bob then immediatelyprepares another pair in jF (þ)l34 and sends its half through thesame channel, which adds the same phase shift f. When the phaseshift is f, the state after the transmission is:

jfl12jfl34 ;1ffiffiffi2p ðjHl1jHl2þ eifjVl1jVl2Þ^

1ffiffiffi2p ðjHl3jHl4

þ eifjVl3jVl4Þ ð2Þ

Because f is unknown, the state actually shared by Alice and Bob isthe following mixed state:

r1234 ;ð

df

2pjfl12kfj^jfl34kfj ð3Þ

If we treat each pair separately, no entanglement is available. Forexample, the marginal state of the pair in modes 3 and 4 is given by:ð

df

2pjfl34kfj ¼

1

2ðjHHl34kHHj þ jVVl34kVV jÞ ð4Þ

where the off-diagonal elements are averaged out and the photonsare obviously not entangled. On the other hand, if both pairs areconsidered together, there still remains an entanglement betweenAlice’s two photons and Bob’s two photons. In fact, it is easy to seethat the whole state r1234 is a classical mixture of an entangled statejHVl13jHVl24þ jVHl13jVHl24 and separable states jHHl13jHHl24

and jVVl13jVVl24: Here the relative phase between the termsjHVl13jHVl24 and jVHl13jVHl24 is not altered by the channelbecause both suffer the same amount of phase shift f.

We can, in principle, extract the entangled component by LOCCin the following way. Alice first performs a collective projectionmeasurement that gives the number of vertically polarized photons,without disclosing the polarization of each photon. If the outcome

of this measurement is unity, the post-measurement state isjHVl13jHVl24þ jVHl13jVHl24; and then Alice and Bob can trans-form this state into an entangled photon pair in the form ofequation (1) by applying local unitary operations. This scheme,called the Schmidt projection method, can be generally applied to npairs of identically dephased photons or those identically preparedin a nonmaximally entangled pure state, with optimal efficiency inthe asymptotic limit6.

Because it is difficult, using current technology, to distinguish thepolarization of a photon without destroying it, the above schemecannot be realized directly. We can, however, achieve almost thesame function using a combination of linear optics and destructivephoton detectors, shown in Fig. 1. Upon receiving the two photons,Alice first rotates the polarization of the photon in mode 3 by 908

using a half-wave plate (HWP3). The photon in mode 1 passesthrough HWP1, which simply adds a phase shift p (HWP1 isinserted for a measurement of a single pair and is not relevant forthe extraction experiment). At this point, the whole state is amixture of jHHl13jHVl24 2 jVVl13jVHl24; jHVl13jHHl24; andjVHl13jVVl24: Alice then mixes the photons in modes 1 and 3with a polarizing beam splitter (PBS) which transmits jHl andreflects jV l. Note that if the state of the photons injected to PBS isjHV l13, mode 5 contains no photons, and if it is jVH l13, it containstwo photons. On the other hand, if it is jHH l13 or jVV l13, itcontains only one photon. Hence, by counting the number ofphotons in mode 5, we can discard the cases jHV l13 and jVH l13.To keep the entanglement in jHHl13jHVl24 2 jVVl13jVHl24; thismeasurement should not distinguish the polarization jHl from jV l.Alice thus rotates the polarization by 458 at HWP5 and detectsphotons on the diagonal basis {jDl5; j �Dl5}; where jDl5 ; ðjHl5þjVl5Þ=

ffiffiffi2p

and j �Dl5 ; ðjHl5 2 jVl5Þ=ffiffiffi2p: Bob also rotates the polar-

ization by 458 at HWP4 and measures the polarization of the photonin mode 4 on the basis {jDl4; j �Dl4}: Then, for example, if Alice findsonly one photon in state jDl5 and Bob finds the photon in jDl4,modes 2 and 6 should contain a photon pair in the maximallyentangled state jFð2Þl62: In this way, Alice and Bob can extractentangled photon pairs by communicating the measurement resultson modes 4 and 5.

In our experiments, photon pairs are generated using the sche-matics shown in Fig. 2. Two pairs of polarization-entangled photons

Figure 1 The schematic diagram of our experiment. Two pairs of polarization-entangled

photons are distributed to Alice and Bob. Before reaching Alice, the photons in modes 1

and 3 pass through the pairwise phase-damping channel (PPC), which gives identical

phase fluctuations to both photons. Alice manipulates the two photons collectively by

using half-wave plates HWP3 and HWP5, a polarizing beam splitter (PBS), and a photon

detector D5. Bob detects a photon in mode 4 with D4 after HWP4 and PBS. HWP3 rotates

the polarization by 908, while HWP5 and HWP4 rotate it by 458. When each of the detectors

D4 and D5 registers a photon, an entangled photon pair is emitted in modes 2 and 6. The

apparatuses inside the dotted boxes are used for verification of the extracted entangled

photon pair in modes 2 and 6. All detectors are silicon avalanche photodiodes, and they

are placed after single-mode optical fibres to select a single spatial mode to ensure a

high visibility. HWP1 is inserted for an auxiliary experiment and it is not relevant here

except for an additional phase shift p.

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are generated by spontaneous parametric down-conversion fromtwo adjacent Type I phase-matched b-barium borate (BBO) crys-tals15,16. In this scheme, the desired entangled photon pairs (1&2 and3&4) are generated whenever there is one photon at each outputport of the non-polarizing beamsplitters. Note that this sourceworks in a nondeterministic way, namely, there is a possibility offailure due to (1) no-photon generation in either or both of theBBOs, (2) channelling of both photons to one side of the beam-splitters, and (3) component losses. Such cases can be discarded by apost-selection, because at least one of modes 1, 2, 3 and 4 containsno photons.

After generating the two pairs of polarization-entangled photons,they are distributed to Alice and Bob. Before reaching Alice, thephotons in modes 1 and 3 pass through the pairwise phase-dampingchannel (PPC), which gives identical phase fluctuations to bothphotons. The PPC is realized experimentally by inserting a liquidcrystal retarder (LCR). It can provide any phase shift between thestates jHl and jV l by changing the applied voltage. Eight differentphases, which are equally spaced from 0 to 2p, are alternated every10 s to simulate the phase-damping channel. Note that this realiza-tion of a PPC with an LCR is equivalent to a more practical situationin which modes 1 and 3 are the two sequential pulses travellingthrough the same optical fibre within the correlation time of thephase fluctuations.

In order to demonstrate that the PPC introduces the phasefluctuations and changes the marginal state of a single pair intothe separable state of equation (4) when the LCR is modulated, weblocked the photons in modes 1 and 2 and measured the corre-lations between the polarizations of photons in modes 3 and 4 inFig. 1 for an unmodulated and a modulated LCR. The results areshown in Fig. 3. We see that the jHl3jHl4 and jVl3jVl4 componentsare dominant. The coherence between these two terms should showup as an interference fringe in the count rate of D4 when we rotate

HWP4, on condition that a photon in state jDl3 (or j �Dl3) is detectedin mode 3. The result shows a visibility of 0.89 when the LCR isunmodulated, implying the creation of highly entangled photonpairs. When the LCR is modulated, visibility becomes less than 0.03,which is a good sign of the loss of coherence. A measurement on thephoton pair in modes 1 and 2 has produced similar results. Theseresults are further supported by the tomographic reconstruction ofthe density matrix17 as shown in Fig. 3c for the modulated LCR.From the reconstructed density matrix for this decohered pair, wecan calculate the entanglement of formation (EOF). EOF is a measureof entanglement taking the value of unity for a maximally entangledqubit pair and zero for separable states. For our decohered photonpair, EOF is calculated to be very small; EOF ¼ 0.0018. This clearlyindicates that the photon pairs shared by Alice and Bob in ourexperiment do not allow the extraction of a highly entangled pair aslong as each pair is manipulated individually.

Figure 2 Experimental set-up for the polarization-entangled photon-pair source.

Spontaneous parametric down-conversion from two adjacent Type I phase-matched,

2-mm-thick b-barium borate (BBO) crystals15,16 generates photon pairs collinearly. The

ultraviolet light beam (average power 360 mW) used for pumping the BBO crystals for PDC

is obtained from a frequency-doubled mode-locked Ti:sapphire laser (wavelength,

790 nm; pulse width, 80 fs; repetition rate, 82 MHz). The polarization of the pump beam is

made diagonal to the axes of BBO using a half-wave plate (HWPUV). After the first photon

pair is generated, the pump beam is reflected back by a dichroic mirror (DMp), and it

passes the BBO in the opposite direction generating the second photon pair which is

picked up by another dichroic mirror (DM). The group delay is compensated by thick

quartz crystals, to erase the information on the origin (the first or the second BBO) of the

photon pair16. The relative phase between H and V polarizations is adjusted by thin quartz

crystals. Each photon pair is then split into two spatial modes by a non-polarizing

beamsplitter to generate entangled photon pairs in modes 1&2 and 3&4. Temporal

overlap of light beams from independent parametric down-conversions is a prerequisite

for high-visibility interference22–24. In our scheme, this is achieved by spectral filtering

using narrow-band interference filters (IF; wavelength, 790 nm; bandwidth, 3.5 nm) as it

has been done in other multiphoton interference experiments2,18–21. The timing between

the photons in modes 1 and 3 is precisely adjusted by mounting the DMp on a motorized

stage.

Figure 3 Experimental results showing that PPC decoheres individual pairs. The modes 1

and 2 are blocked, and the photons in modes 3 and 4 are measured after passing through

the PPC. The axis of HWP5 is adjusted so that it does not rotate the polarization. Then

polarization correlations are recorded by coincidence counting between detectors D5 and

D4 for various angles of HWP3 and HWP4. a, b, Typical coincidence measurements for

unmodulated and modulated LCR, respectively. Left, coincidence rates on the {jH l; jV l}basis. Right, the rate of coincidence events where a photon in polarization jDl (or j �Dl) is

detected at D5 and a linearly polarized photon with angle v is detected at D4 (v ¼ 08,

v ¼ 458, v ¼ 908 and v ¼ 1358 correspond to jH l, jD l, jV l and j �Dl; respectively). The

solid curve is the best fit to the data by two sine functions with the same amplitude. The

observed visibility is 0.89 in a and less than 0.03 in b. c, Real and imaginary components

of the density matrix. Reconstruction is done by recording polarization correlations

measured on 16 different settings of HWP3, HWP4 and additionally inserted quarter-wave

plates in modes 3 and 4. This density matrix is close to the state in equation (4). The

entanglement of formation ( EOF) calculated from the density matrix is 0.0018.

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Now we will show that the collective manipulation shown in Fig. 1can extract an entangled photon pair in modes 2 and 6 by selectingthe cases where a photon in state jDl5 is observed in mode 5 and aphoton in jDl4 is observed in mode 4. Because our source ofentangled pairs based on parametric down-conversion in Fig. 2 isnondeterministic, we should post-select the events where both ofthe photon detectors at modes 2 and 6 register a photon. Hence,what we have measured is a fourfold coincidence at detectors D2,D4, D5 and D6. In this case, there is no need to distinguish the arrivalof two photons in mode 5, because such events (no photons in mode6) are discarded by the post-selection. The results of the polarizationcorrelations for the selected photon pair in modes 2 and 6 are shownin Fig. 4. In contrast to Fig. 3b, it clearly shows an interferencefringe. Visibility is found to be 0.63 ^ 0.05, which is well above theachievable value of 0.5 in the classical model. We believe that thevisibility is limited mainly by the residual temporal and spatialmode mismatch between the photons belonging to different pairs,as is the case in other interference experiments2,18–21 and theoreticalstudies22–24.

The rate of the fourfold coincidence rate is quite low, so we havenot collected enough data sets to reconstruct the density matrix ofthe extracted pair. Nevertheless, we can still set a bound25 to thefidelity f of the extracted pair to the state jF (2)l62 as 0:78^ 0:05 #

f # 0:89^ 0:02; from the observed correlations on {jHl; jVl} and{jDl; j �Dl} bases. The lower bound of the fidelity can then be used todetermine a lower bound for EOF7, which turns out to be EOF $

0:42^ 0:12: The extracted photon pair in our experiment is thusclearly shown to be entangled.

The collective operation on two photons used in our experimentto extract entanglement is essentially the one referred to as quantumparity check26,27. This feature was originally proposed in ref. 28, andforms an important building block for quantum informationprocessing by linear optics11,29,30. Our experiment has shown thatthe quantum parity check can be applied to a nontrivial task, and wehope that this demonstration forms a step towards experimentalrealizations of more complicated applications in quantum com-munication and computation. A

Received 25 October; accepted 29 November 2002; doi:10.1038/nature01358.

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Acknowledgements We thank K. Nagata, K. Tamaki, A. Miranowicz and J. Shimamura for

helpful discussions.

Competing interests statement The authors declare that they have no competing financial

interests.

Correspondence and requests for materials should be addressed to N.I.

(e-mail: imoto@soken.ac.jp).

Figure 4 Experimental results showing that the extracted photon pair is entangled.

Polarization correlations between the photon pair in modes 2 and 6 are taken on condition

that the detectors D4 and D5 both register a photon. The left shows coincidence rates on

the {jHl; jV l} basis. The right is the rate of coincidence events where a photon in

polarization jD l (or j �Dl) is detected at D6 and a linearly polarized photon with angle v is

detected at D2. The error bars assume the Poisson statistics of the events. The solid curve

represents the best fit to the data. The observed visibility 0.63 ^ 0.05 demonstrates that

the photons in modes 2 and 6 are entangled. The lower bound of fidelity to the state

jF (2) l62 is 0.78 ^ 0.05, from which the lower bound of EOF is calculated as

0.42 ^ 0.12.

letters to nature

NATURE | VOL 421 | 23 JANUARY 2003 | www.nature.com/nature346