Entangling Independent Photons by Time Measurement
Halder_articleFigureArxiv
Entangling Independent Photons by Time Measurement 
Matthäus Halder, Alexios Beveratos, Nicolas Gisin, Valerio Scarani, Christoph Simon 
& Hugo Zbinden  
Group of Applied Physics, University of Geneva, 20, rue de l'Ecole-de-Médecine, 1211 
Geneva 4, Switzerland 
A quantum system composed of two or more subsystems can be in an entangled 
state, i.e. a state in which the properties of the global system are well defined but 
the properties of each subsystem are not. Entanglement is at the heart of quantum 
physics, both for its conceptual foundations and for applications in information 
processing and quantum communication. Remarkably, entanglement can be 
“swapped”: if one prepares two independent entangled pairs A1-A2 and B1-B2, a 
joint measurement on A1 and B1 (called a “Bell-State Measurement”, BSM) has 
the effect of projecting A2 and B2 onto an entangled state, although these two 
particles have never interacted or shared any common past1,2. Experiments using 
twin photons produced by spontaneous parametric down-conversion (SPDC) have 
already demonstrated entanglement swapping3-6, but here we present its first 
realization using continuous wave (CW) sources, as originally proposed2. The 
challenge was to achieve sufficiently sharp synchronization of the photons in the 
BSM. Using narrow-band filters, the coherence time of the photons that undergo 
the BSM is significantly increased, exceeding the temporal resolution of the 
detectors. Hence pulsed sources can be replaced by CW sources, which do not 
require any synchronization6,7, allowing for the first time the use of completely 
autonomous sources. Our experiment exploits recent progress in the time precision 
of photon detectors, in the efficiency of photon pair production by SPDC with 
waveguides in nonlinear crystals8, and in the stability of narrow-band filters. This 
approach is independent of the form of entanglement; we employed time-bin 
entangled photons9 at telecom wavelengths. In addition to entangling photons from 
autonomous sources, a fundamental quantum phenomenon, our setup is robust 
against thermal or mechanical fluctuations in optical fibres thanks to cm-long 
coherence lengths. The present experiment is thus an important step towards real-
world quantum networks with truly independent and distant nodes. 
The BSM is the essential element in an entanglement-swapping experiment. 
Linear optics allows the realization of only a partial BSM10 by coupling the two 
incoming modes on a beam-splitter (BS) and observing a suitable detection pattern in 
the outgoing modes. Such a measurement is successful in at most 50% of the cases. 
Still, a successful partial BSM entangles two photons that were, up to then, independent. 
The physics behind this realization is the bosonic character of photons, it is therefore 
crucial that the two incoming photons are indistinguishable: they must be identical in 
their spectral, spatial, polarization and temporal modes at the BS: Spectral overlap is 
achieved by the use of similar filters, spatial overlap by the use of single-mode optical 
fibres and polarization is matched by a polarization controller. In addition, the temporal 
resolution must be unambiguous: detection at a time t ± ∆td, with ∆td the temporal 
resolution of the detector, must single out a unique time mode. In previous experiments, 
synchronised pulsed sources created both the photons at the same time and path lengths 
had to be matched to obtain the required temporal overlap. The pulse length, i.e. the 
coherence length of the photons, was τc << ∆td (typically τc <1ps), but two subsequent 
pulses were separated by more than ∆td11. The drawback of such a realization is that the 
two sources cannot be totally autonomous, because of the indispensable 
synchronization. Here, by using stable narrow-band filters and detectors with low jitter, 
we reach the regime where τc > ∆td12. In this case, the detectors always single out a 
unique time mode. As a benefit, we can give up the pulsed character of the sources and 
the synchronization between them, realizing for the first time the entanglement 
swapping scheme as originally proposed in Ref.2. 
The experimental scheme is sketched in Fig.1. Each of the two non-linear crystals 
emits pairs of energy-time entangled photons13 produced by SPDC of a photon 
originating from a CW laser. A pair can be created at any time t, and all these processes 
are coherent within the km-long coherence length of the laser: 
tt,ψ describes a pair of signal and idler photons emitted by source A. Thus, 
the state produced by two independent sources can conveniently be represented as 
( )∑ ∑ 
++++++∝=Ψ
BABABABAprep
tttttttttttt
,,,,,,
ττττψψ .
The first term in the above sum describes 4 photons all arriving at the same time t at a 
BS. Since for this case two identical photons bunch in the same mode, due to their 
bosonic nature, this term leads to a Hong-Ou-Mandel (HOM) dip14. The second term 
describes two photon pairs arriving with a time difference τ>0. The two photons A1 and 
B1 are sent through a 50/50 BS. This fibre-coupler and the two detectors behind it 
realize a partial BSM10: in particular, when one of the detectors fires at time t and the 
other one at time t+τ, this corresponds to a measurement of the Bell-state −Ψ  for A1 
and B19. In consequence the remaining two photons A2 and B2 are projected in the 
state 
22222222 BABABABA
tttt ττψ +−+∝Ψ≡ − , which is a singlet state for 
time-bin entanglement. Hence entanglement has been swapped. This process can be 
seen as teleportation15-19 of entanglement. It can be tested by sending the photons in 
unbalanced interferometers such that the path difference between the two arms 
corresponds to τ. Interference between temporally distinguishable events (at t and t+τ, 
respectively) is obtained by erasing the time information via unbalanced 
interferometers9,12,20 as shown in Fig.1. Note that the value of τ varies from one 
successful entanglement swapping event to another. As in our experiment the path 
differences of the analysing interferometers are fixed, we test the entanglement of the 
swapped pairs produced with one fixed τ.  
We now describe our experiment in more detail. Above we have assumed that the 
detection times t and t+τ of the BSM are sharply defined. In physical terms, this 
requirement means that the detection times have to be determined with sub-coherence-
time precision: this is the key ingredient that makes it possible to achieve 
synchronisation of photons A1 and B1 by detection, thus to use CW sources. Since 
single-photon detectors have a certain intrinsic minimal jitter, the coherence length of 
the photons has to be increased to exceed this value by narrow filtering.  
Consider the case where each of the two sources emits one entangled pair of 
photons, and where A1 and B1 take different exits of the BS. The photon that takes 
output port 1 is detected by a NbN superconducting single-photon detector (SSPD)21 
with a time resolution ∆td = 74ps. The photon in output port 2 is detected by an InGaAs 
single photon avalanche diode (APD, ∆td = 105ps) triggered by the detection in the 
SSPD. The time resolution of these detectors is several times smaller than that of 
commercial telecommunication photon detection modules. To enable synchronization of 
the photons at the BS by post-selection, the coherence length of the photons has to 
exceed ∆td. This is achieved by using filters of 10pm bandwidth, corresponding to a 
coherence time τc of 350ps. We are able to tolerate the losses due to filtering because 
we use cm-long wave guides in PPLN crystals with a high down-conversion efficiency 
of 5*10-7 per pump photon and per nm of the created spectrum. For 2mW of laser 
power, an emission flux q of 2*10-2 pairs per coherence time is obtained. This q is 
independent of the filtered bandwidth: in fact, narrower filtering decreases the number 
of photons per second but increases their coherence time by the same factor, hence 
keeping q constant. 
Any two-detector click in the BSM prepares the two remaining photons in a time-
bin entangled state. In our experiment the creation rate for such entangled photon pairs 
is ≈104 per second, with time delays τ ranging up to 10ns. This is two orders of 
magnitude larger than in previous experiments at shorter and similar wavelengths3-6. As 
the probability of both the pairs originating from different sources equals the probability 
of creating them in the same source, the first cases have to be post selected by 
considering only 4-fold-events. Furthermore only one fixed τ is tested. The resulting 
rate is smaller by two orders of magnitude compared to the creation rate. To verify their 
entanglement, the two photons are sent through unbalanced interferometers (a and b) in 
Michelson configuration. The path length differences of the interferometers must be 
identical only within the coherence length of the analyzed photons (7cm), but stable in 
phase (α and β): this is achieved by active stabilization22. On each side, both output 
ports of the interferometer are connected to InGaAs APD, triggered by the detection of 
both the photons in the BSM.  
Four-fold coincidences, between one click in each BSM detector and one behind 
each interferometer, are registered by a multistop time to digital converter (TDC) and 
the arrival times (t, t+τ) are stored in a table. For τ = 0, we observe a decrease in this 
coincidence count rate (see Fig.2). The visibility of this HOM dip of 77% indicates the 
degree of indistinguishability of the two photons A1 and B1 and could be further 
improved by increasing τc/∆td. The width of the dip corresponds to the convolution of τc 
for the two photons with the jitter of the detectors. Note that photons which are detected 
after the BS at measurable different times, but within τc, do still partially bunch, which 
confirms that the relevant time precision is set by the coherence time of the photons. 
To test for successful entanglement swapping, the relative phase α-β between the 
interferometers is changed by keeping α fixed and scanning β. As usual for the analysis 
of time-bin entanglement9, interference is observable in the case where, at the output of 
the interferometers, both photons are detected at the same time.  
We measured the four possible 4-fold coincidence count rates ),( βαijR  (clicks in 
two outer detectors conditioned on a successful BSM) with { }−+∈ ,, ji  the different 
detectors behind interferometer a and b, respectively. Thus the two-photon spin-
correlation coefficient 
),(),(),(),(
),(),(),(),(
βαβαβαβα
βαβαβαβα
−−+−−+++
−−+−−+++
E  is 
obtained as a function of the phase settings α and β and plotted in Fig.3 for α fixed. A fit 
of the form )cos(),( βαβα −= VE  to our experimental data gives a visibility V=0.63. 
If one assumes that the two photons are in a Werner state (which corresponds to white 
noise), one can show that 31>V  is sufficient to demonstrate entanglement
5,23. Our 
experimental visibility clearly exceeds this bound24. The plain squares show that the 3-
fold coincidence count rate between a successful BSM and only one of the outside 
detectors is independent of the phase setting, as expected for a −Ψ -state. V is limited by 
imperfections in the matching of wavelengths, polarisations and temporal 
synchronisation. In our setup, the latter is the main source of errors. The integration 
time of this measurement was 1 hour for each of the 13 phase settings and the 
experiment was run 8 times, hence took 104 hours, which demonstrates the stability of 
our setup. Such long integration times are necessary because of low count rates (5 four-
fold coincidences per hour), which are mainly due to poor coupling efficiencies of the 
photons into optical fibres, losses in optical components like filters and interferometers, 
as well as the limited detectors efficiencies. All these factors decrease the probability of 
detecting all four photons of a two-pair event. 
Exploiting all the produced entangled pairs with different delays τ is possible in 
principle using rapidly adjustable delays in the interferometers or quantum memories. 
This would be an important step towards the realization of recent proposals for long-
distance quantum communication25. Time-bin entanglement is particularly stable and 
well suited for fibre optic communications26, and the coherence length of 7cm allows 
tolerating significant fiber length fluctuations as expected in field experiments. If 
additionally, count rates are further improved, long distance applications like quantum 
relays27,28 become realistic. 
In conclusion, we realized an entanglement swapping experiment with completely 
autonomous CW sources. This is possible thanks to the low jitter of new NbN 
superconducting and InGaAs avalanche single-photon detectors and to the long 
coherence length of the created photon pairs after narrow-band filtering. The setup does 
not require any synchronization between the sources and is highly stable against length 
fluctuations of the quantum channels. 
Methods 
Schematic description of the setup. Both sources consist of an external cavity diode 
laser in CW mode at 780.027nm (Toptica DL100), stabilized against a Rubidium 
transition (85Rb F = 3), pumping a nonlinear periodically poled Lithium Niobate 
waveguide8 (PPLN, HC photonics Corp) at a power of 2mW. The process of SPDC 
creates 4*1011 pairs of photons per second with a spectral width of 80nm FWHM 
centered at 1560nm. The photons are emitted collinearly and coupled into a single-mode 
fiber with 25% efficiency and the remaining laser light is blocked with a silicon high-
pass filter (Si). Signal and idler photons are separated and filtered down to a bandwidth 
of 10pm by custom-made tunable phase-shifted Bragg gratings (AOS GmbH). These 
filters have a rejection of >40dB, 3dB insertion losses, and can be tuned independently 
over a range of 400pm. Once a signal photon has been filtered to ωs, the corresponding 
idler photon has a well-defined frequency ωi, due to stabilized pump wavelength and 
energy conservation in the process of SPDC (ωs + ωi = ωlaser). After filtering, the 
effective conversion efficiency for creating a photon pair within these 10pm is 5*10-9 
per pump photon. In principle, the available pump power permits us to produce narrow 
band entangled photon pairs at rates up to 3*108 pairs per second, which translates to an 
emission flux of more than 0.1 photons per coherence time. In this experiment, we 
limited the laser to 2mW, in order to reduce the probability of multiple pair creation 
which would decrease the interference visibility29.  
After the beam splitter (BS), the first photon is detected by a NbN 
superconducting single-photon detector (SSPD, Scontel) operated in free running 
mode21, with a total detection efficiency of 4.5%, 300 dark counts/sec and a timing 
resolution of 74ps, including the time jitter of both the detector and the amplification 
and discrimination electronics. The second photon is detected by an InGaAs single-
photon avalanche diode operated in Geiger mode and actively triggered by the detection 
in the SSPD. With home-made electronics this detector has a time jitter of 105ps. The 
observed HOM-dip with a visibility of 77% was obtained with two SSPD detectors, 
which were used because of their smaller time jitter. For the entanglement swapping, we 
used an APD, because of its higher efficiency, in order to shorten the integration time. 
This means that the visibility of the interference fringe in Fig.3 could further be 
increased by the use of two SSPDs, but with the drawback of longer measurement 
times. 
Photons A2 and B2 are also detected by InGaAs APDs (ID200, idQuantique). All 
the APDs have quantum efficiencies of 30% and dark count probabilities of 10-4 per ns. 
The interferometers are actively stabilized against a laser locked on an atomic transition, 
have a path length difference of 1.2ns and insertion losses of 4dB each.  
1. Yurke, B. & Stoler, D. Bell’s-inequality experiments using independent-particle 
sources. Phys. Rev. A 46 2229 (1992). 
2. Żukowski M., Zeilinger A., Horne M. A. & Ekert A. K. ”Event-ready-detectors” Bell 
experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287-4290 (1993). 
3. Pan J.-W., Bouwmeester D., Weinfurter H. & Zeilinger A. Experimental 
Entanglement Swapping: Entangling Photons That Never Interacted. Phys. Rev. Lett. 
80, 3891-3894 (1998). 
4. Jennewein T., Weihs G., Pan J.-W. & Zeilinger A. Experimental Nonlocality Proof of 
Quantum Teleportation and Entanglement Swapping. Phys. Rev. Lett. 88, 017903 
(2002). 
5. de Riedmatten, H., Marcikic, I., Tittel, W., Zbinden, H. & Gisin, N. Long-distance 
entanglement swapping with photons from separated sources. Phys. Rev. A 71, 050302 
(2005). 
6. Yang, T. et al. Experimental Synchronization of Independent Entangled Photon 
Sources. Phys. Rev. Lett. 96, 110501 (2006). 
7. Kaltenbaek, R., Blauensteiner, B., Żukowski, M., Aspelmeyer, M., & Zeilinger A. 
Experimental interference of independent photons. Phys. Rev. Lett. 96, 240502 (2006). 
8. Tanzilli S. et al. PPLN waveguide for quantum communication. Eur. Phys. .J D 18, 
155 (2002). 
9. Brendel, J., Gisin, N., Tittel, W. & Zbinden, H. Pulsed Energy-Time Entangled Twin-
Photon Source for Quantum Communication. Phys. Rev. Lett. 82, 2597 (1999). 
10. Weinfurter, H. Experimental Bell-State Analysis. Europhys Lett. 25, 559 (1994). 
11. Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575 
(1997). 
12. Legero, T., Wilk, T., Henrich, M., Rempe, G. & Kuhn, A. Quantum Beat of Two 
Single Photons. Phys. Rev. Lett. 93, 070503 (2004). 
13. Franson, J.D. Bell inequality for position and time. Phys. Rev. Lett. 62, 2205 (1989). 
14. Hong, C.K., Ou, Z.Y. & Mandel, L. Measurement of Subpicosecond Time Intervals 
between Two Photons by Interference. Phys. Rev. Lett. 59, 2044 (1987). 
15. Furusawa, A. Unconditional Quantum Teleportation. Science 282, 706 (1998) 
16. Boschi, D.,Branca, S., De Martini, F., Hardy, L. & Popescu, S. Experimental 
Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and 
Einstein-Podolsky-Rosen Channels. Phys. Rev. Lett. 80, 1121 (1998). 
17. Marcikic, I., de Riedmatten, H., Tittel, W., Zbinden, H. & Gisin, N. Long-distance 
teleportation of qubits at telecommunication wavelengths. Nature 421, 509 (2003). 
18. Riebe, M. et al. Deterministic quantum teleportation with atoms. Nature 429, 734 
(2004). 
19. Barrett, M. D. et al. Deterministic quantum teleportation of atomic qubits. Nature 
429, 737 (2004). 
20. Pittman, T. B. et al. Can Two-Photon Interference be Considered the Interference of 
Two Photons? Phys. Rev. Lett. 77, 1917 (1996). 
21. Milostnaya, I. et al. Superconducting single-photon detectors designed for operation 
at 1.55-µm telecommunication wavelength. J. Phys. Conference Series 43, 1334 (2006). 
22. Marcikic, I. et al. Distribution of Time-Bin Entangled Qubits over 50 km of Optical 
Fiber. Phys. Rev. Lett. 93, 180502 (2004). 
23. Peres, A. Separability Criterion for Density Matrices. Phys. Rev. Lett. 77, 1413 
(1996). 
24. In fact, in our experimental situation entanglement is present even for values of V 
that are smaller than 0.33 because the noise is dominated by phase errors due to the 
partial distinguishability of the two photons involved in the BSM. 
25. Duan, L.-M., Lukin, M.D., Cirac, J.I. & Zoller, P. Long-distance quantum 
communication with atomic ensembles and linear optics. Nature 414, 413 (2001). 
26. Thew R. T., Tanzilli S., Tittel W., Zbinden H., & Gisin N. Experimental 
investigation of the robustness of partially entangled qubits over 11 km. Phys. Rev. A 
66, 062304 (2002). 
27. Jacobs B. C., Pittman T. B. & Franson J. D. Quantum relays and noise suppression 
using linear optics. Phys. Rev. A 66, 052307 (2002). 
28. Collins, D., Gisin, N. & de Riedmatten, H. Quantum Relay for Long Distance 
Quantum Cryptography. J. Mod. Opt. 522, 735 (2005). 
29. Scarani, V., de Riedmatten, H., Marcikic, I., Zbinden, H. & Gisin, N. Four-photon 
correction in two-photon Bell experiments. Eur. Phys. J. D 32, 129 (2005). 
Acknowledgements: We thank C. Barreiro, J.-D. Gautier, G. Gol’tsman, C. Jorel, S Tanzilli and J. van 
Houwelingen for technical support, and H. de Riedmatten, S. Iblisdir and R. Thew for helpful 
discussions. Financial support by the EU projects QAP and SINPHONIA and by the Swiss NCCR 
Quantum Photonics is acknowledged. 
Author Information: Reprints and permissions information is available at 
npg.nature.com/reprintsandpermissions. The authors declare that they have no competing financial 
interests Correspondence and requests for materials should be addressed to M.H. 
(matthaeus.halder@physics.unige.ch). 
Figure 1: 
Experimental 
Setup. Two 
pairs of 
entangled 
photons (A1-
A2 and B1-B2) 
are produced, 
one by each source (A and B), and all the photons are narrowly filtered (10pm). 
One photon of each pair is sent into a 50/50 beam splitter (BS) and both 
undergo a partial Bell-State measurement (BSM). By detection in different 
output ports of BS and with a certain time delay τ the two photons A1 and B1 
are projected on the 
−Ψ -state for time bin qubits, projecting the two remaining 
photons on the 
−Ψ -state as well. The entanglement is swapped onto the 
photons A2 and B2 and can be tested by passing them through interferometers 
with phases α and β, and detecting them by single photon avalanche detectors 
(APD) in both outputs (+,-) of each interferometer. 
 Figure 2: 4-fold 
coincidence count rate as 
a function of the temporal 
delay τ. It can be seen, 
that the detection 
probability decreases if 
the two photons A1 and 
B1 arrive simultaneously 
(τ=0) at the beam splitter 
due to photon bunching, leading to a Hong-Ou-Mandel dip with 77% visibility.  
Figure3  
Figure 3: The correlation coefficient E(α,β) between photons A2 and B2, 
conditioned on a BSM of photons A1 and B1, as a function of the relative phase 
α–β of the interferometers (open points). A fit of the form )cos(),( βαβα −= VE  
gives a visibility V=0.63. This proves successful entanglement swapping (see 
text). The coincidence count rate of only one detector conditioned on a 
successful BSM (3-fold coincidence) is independent of the phase setting as 
expected for a −Ψ -state (squares).
