Abstract
Entanglement swapping at telecom wavelengths is at the heart of quantum networking in optical fiber infrastructures. Although entanglement swapping has been demonstrated experimentally so far using various types of entangled photon sources both in nearinfrared and telecom wavelength regions, the rate of swapping operation has been too low to be applied to practical quantum protocols, due to limited efficiency of entangled photon sources and photon detectors. Here we demonstrate drastic improvement of the efficiency at telecom wavelength by using two ultrabright entangled photon sources and four highly efficient superconducting nanowire single photon detectors. We have attained a fourfold coincidence count rate of 108 counts per second, which is three orders higher than the previous experiments at telecom wavelengths. A raw (net) visibility in a HongOuMandel interference between the two independent entangled sources was 73.3 ± 1.0% (85.1 ± 0.8%). We performed the teleportation and entanglement swapping and obtained a fidelity of 76.3% in the swapping test. Our results on the coincidence count rates are comparable with the ones ever recorded in teleportation/swapping and multiphoton entanglement generation experiments at around 800 nm wavelengths. Our setup opens the way to practical implementation of deviceindependent quantum key distribution and its distance extension by the entanglement swapping as well as multiphoton entangled state generation in telecom band infrastructures with both space and fiber links.
Introduction
Distribution of quantum entanglement through optical channels is the basis of implementing quantum information and communication protocols, which do not have any classical counterparts, such as deviceindependent quantum key distribution (DIQKD)^{1,2}, quantum secret sharing^{3,4}, quantum repeater network^{5,6,7,8,9} and so on. The distance of direct transmission of entanglement is, however, severely limited, because the entanglement is easily destroyed by the channel loss and channel noises. Extending the distance and networking the entanglement requires entanglement swapping as the very elementary protocol. This is to convert two independent entangled photon pairs, say, photons A and B and C and D, to a new entangled pair of photons between A and D, those are not originally entangled, by performing a Bell measurement on photons B and C.
Practical methods for the swapping at present is to prepare entangled photons from spontaneous parametric down conversion (SPDC), to detect the two photons at the intermediate node by two singlephoton detectors and to herald the success event for the swapping. Thus the protocol is probabilistic. Its success rate is directly determined by the fourfold coincidence count (4fold CC) rate.
The first entanglement swapping experiment was carried out in 1998, with SPDC process in BBO crystal^{10}. Since then, many proofofprinciple experiments have been demonstrated at near infrared wavelength range (around 800 nm)^{9,10,11}. Demonstrations at telecom wavelengths (around 1550 nm) have also been demonstrated with SPDC in bulk crystals^{12,13,14}, in waveguides^{15,16,17}, or with spontaneous fourwave mixing (SFWM) in fibers^{18}. Unfortunately, however, the efficiencies were very low, especially at telecom wavelengths so far. For example, the maximum 4fold CC rate has been 0.08 counts per second (cps)^{14}. This limits practical applications of entanglement swapping to quantum information and communication protocols.
In this work, we demonstrate highly efficient entanglement swapping by utilizing our highquality entangled photon source^{19} and highly efficient superconducting nanowire single photon detectors (SNSPDs)^{20,21}. In our experiment, 4fold CC rate of 108 cps was attained, which is three orders higher than the previous record^{14}. A net visibility is 85.1 ± 0.8% in HongOuMandel interference between two independent entangled sources. We also demonstrate high quality teleportation experiment, with 2fold CC of 150 kcps, which is comparable to those obtained in highly efficient schemes in the nearinfrared wavelengths^{22,23,24,25} and with the entanglement visibility of 98%, which is the highest among^{22,23,24,25}.
Experiment and Results
The experimental setup is shown in Fig. 1. The entangled photon source is based on a SPDC from a groupvelocitymatched periodically poled KTiOPO_{4} (GVMPPKTP) crystal in a Sagnaloop configuration^{19}. This entangled photon source has a spectral purity as high as 0.82^{26}, which can widen applications with multisource of entangled photons. The SNSPD has a maximum system detection efficiency (SDE) of 79% with a dark count rate (DCR) of 2 kcps. For more details of this SagancGVMPPKTP entangled source, refer to Refs. 19, 27, 28. By carefully improving the coupling efficiency, we have improved the coincidence counts from 20 kcps (in Ref. 19) to 40 kcps, at 10 mW pump power. The overall efficiency, which is the product of all efficiencies between the source and detectors, was improved from 0.10 (in Ref. 19) to 0.20. Further, the minimal interference visibility in polarization correlation measurement was improved from ~96% (in Ref. 19) to ~98% at 10 mW pump power, by finely optimizing the alignment in the Sagnacloop.
The entangled source
First, we perform the photon polarization correlation measurement with the setup shown in Fig. 1(a). Both the source I and source II are prepared in state. With pump powers of 80 mW for source I and 85 mW for source II, we achieve coincidence counts of around 150 kcps, as shown in Fig. 2, corresponding to 300 kcps without the polarizers. The corresponding mean photonpair numbers per pulse are around 0.1 for both sources. The raw visibilites are around 87%, while the background subtracted visibilities (i.e., net visibilities) are around 98% for each polarizers set for source II. The degradation of this visibility at high pump power is mainly caused by the multipair emission. The result agrees with the theoretical model in Ref. 28 which includes multiphoton emissions and system imperfections (see Methods). These highbrightness entangled photon sources guarantee the high count rate in the following teleportation and entanglement swapping experiments.
HongOuMandel interference
Next, we measure a fourfold HongOuMandel (HOM) interference^{29} between ch1 and ch4 (heralded by ch2 and ch3) with 4 polarizers inserted in each channel in Fig. 1(b). The polarization angles for θ_{1}–θ_{4} are set at 0°/90°/90°/0°, respectively. Firstly, we test the HOM interference with no bandpass filters inserted, whose result is shown in Fig. 3(a). The 4fold CC is 169 cps (5080 counts in 30 s) and the raw visibility is 67.1 ± 0.9%. The background counts is mainly caused by the multipair emission in SPDC. We subtract the background counts using the same method as shown in Ref. 30. We block only ch1 and measure 4fold CCs, then block only ch4 and measure 4fold CCs. The sum of these two coincidence counts constitutes the background count. After background subtraction, the net visibility is 78.4 ± 0.8%, which is consistent with our previous results in Ref. 30.
To further increase the visibility, we should improve the spectral purity of photons. As reported in Ref. 26, the downconverted photons from our PPKTP crystal have an intrinsic spectral purity of 0.82 and this value can be improved to unity by inserting coarse bandpass filters (CBPFs) to cut the side lobes in the joint spectral amplitude. In this experiment, we prepared four CBPFs which have nearGaussian shape with FWHM (full width at half maximum) of 2.1 nm and peak transmission efficiency of 93% at the central wavelength of 1584 nm. The overall transmittance efficiency of the CBPFs is around 77%, tested with our downconverted photons, which have spectra of Gaussian shape with FWHM of 1.2 nm and center wavelength of 1584 m. We insert two CBPFs in ch1 and ch4 and repeat the HOM interference, whose result is shown in Fig. 3(b). The 4fold CC rate is 108 cps (3249 counts in 30 s) and the raw visibility is 73.3 ± 1.0%. After subtracting the background multiphoton emission, the net visibility is 85.1 ± 0.8%. The raw (net) visibility was improved by 6.2% (6.7%) after the insertion of the two CBPFs, due to the increase of the spectral purity. However, this visibility improvement is lower than our expectation (net visibility ≈100%), which may be caused by the following reasons: the photons generated from two different nonlinear crystals may have different spectral properties; the transmission profiles of these CBPFs can not be perfectly the same, which may also lead to the difference of the transmitted photons; a small portion of the sidelodes may be not filtered because the transmission shape of the CBPFs is not in a perfect Gaussianshape.
We also investigate the HOM interference with four CBPFs inserted in each channel, whose result is shown in Fig. 3(c). The 4fold CC rate is 78 cps (2329 in 30 s) and the raw (net) visibility is 75.6 ± 1.1% (87.2 ± 0.8%). The raw (net) visibility was improved by 2.3% (2.1%) after the insertion of these two more CBPFs. In the following test of quantum teleportation and entanglement swapping, all these four CBPFs are inserted.
Quantum teleportation
After the test of HongOuMandel interference, we remove Polarizer 1 (θ_{1}) and Polarizer 4 (θ_{4}), then the setup in Fig. 1(c) is ready for the test of quantum teleportation. The principle of teleportation in our experiment is as follow. Assume photons in ch1 are in an initial state of i〉_{1} = (αH〉 + βV〉)_{1} and photons in ch3 and ch4 are in an entangled state of . A partial Bell state measurement on photons in ch1 and ch4 will teleport the state i〉_{1} to the photons in ch3, i.e., the final state of the photons in ch3 will be f〉_{3} = (αH〉 + βV〉)_{3}. This process can be expressed as^{31}:
where and are the four Bell states. We only focus the second term:
In this process, the partial Bell state measurement is realized by coincidence counting after a beam splitter (i.e., FBS in Fig. 1(c)), due to the fact that only one input state, ψ^{−}〉, out of the four Bell states has coincidence counts after the beam splitter. The state of the photons in ch1 is heralded by the photon states in ch2 with the correlation of , where, (corresponding to θ = 45°) and (corresponding to θ = 135°).
First, we demonstrate a teleportation in H/V bases, as shown in Fig. 4(a) and (b). The initial state of the photons in ch1 is in H polarization, i.e., i〉_{1} = H〉_{1}, which is heralded by their daughter photons in ch2 with V polarization (θ_{2} = 90°). Then, the partial Bell state measurement on ch1 and ch4 projects the correlated photons in ch3 with H polarization, i.e., f〉_{3} = H〉_{3}. With this condition, if the angle of Polarizer 3 is θ_{3} = 0°, the 4fold CC exists, therefore, no HOM dip appears at the zero delay point, as shown in Fig. 4(b). Otherwise, if θ_{3} = 90°, all the Hpolarized photons are blocked, then ideally, there is no 4fold CC at the zero delay point, so a HOM dip occurs, as shown in Fig. 4(a). Similarly, we also showed the teleportation results with other bases, as shown in Fig. 4(c) and (d) for ch1 at D〉 bases (with θ_{2} = 45°). More results are summarized in Tab. 1. The visibilities in H/H, V/V, A/A, D/D bases range from 75.8% to 84.9%, all well beyond the classical limit of 50%. These results demonstrate the potential of our setup for highly efficient quantum teleportation. To fully verify the nonclassicality of quantum teleportation, one has to perform the experiment with two more states ().
It should be noted that from the coincidence counts in Fig. 4(a–d), we can see the SNSPDs are strongly polarizationdependent. Because of its special construction structure, the SNSPD has a maximal efficiency on certain polarization direction and its orthogonal direction has the minimal efficiency. According to our experimental tests, the maximal efficiency is typically two times of the minimal efficiency. To avoid the polarizationdependency of the SNSPDs for the entanglement swapping test, we change the FBS in Fig. 1(c) to the combination of a FBS and a FPBS in Fig. 1(d).
Entanglement swapping
The principle of entanglement swapping can be understood from the following equation^{32}:
The detection of an entangled state in ch1 and ch4 heralds the existence of entanglement in ch2 and ch3, which originally have no correlation. The partial Bell state measurement in Fig. 1(d) is realized by the combination of FBS and FPBS. Only one input state ψ^{+}〉 out of the four Bell states has coincidence counts at port 7 and port 8 in Fig. 1(d), due to the transformation of a BS: .
To realize such a scheme in experiment, we need to firstly calibrate the photon polarizations in the FBS and FPBS. We reinsert Polarizer 1 and Polarizer 4 and rotate the angles of HWPs and QWPs in ch1 and ch4, so as to achieve the following condition: the H polarized photons in ch1 travel to outport 8, while the H polarized photons in ch4 travel to outport 7. Under this condition, the H (V) polarized photons in ch4 are converted to V (H) polarized, while the polarization of photons in ch1 is not changed and hence can function as a reference. Therefore, an input state of ϕ^{±}〉_{14} is transformed to the state of ψ^{±}〉_{14} and the ψ^{±}〉_{14} state is transform to ϕ^{±}〉_{14} state, respectively. As a result, the state in Eq. (3) is transformed to Eq. (4):
Let us focus on the third term. The ψ^{+}〉_{14} state will be detected by the Bell state analyzer and thus projects the state in ch2 and ch3 to ϕ^{+}〉_{23} state.
After the calibration, Polarizer 1 and Polarizer 4 are removed. We fix the optical path delay at the zero delay position, then we rotate θ_{2}/θ_{3} and record the 4fold CC, whose result is shown in Fig. 5 (a). Figure 5 (a) shows an experimental interference pattern of ϕ^{+}〉_{23} state, which is consistent with our theoretical expectation in Eq. (4). The net (raw) visibilities at θ_{2} = 0°/45°/90°/135° are 90.6% (78.0%)/65.7% (56.1%)/87.4% (74.6%)/63.6% (54.4%), respectively. The background counts are subtracted using the same method as described in the fourfold HOM interference.
To decrease the effect of multiphoton emission, we decrease the pump power in Fig. 5(b) to half of the power in Fig. 5(a), i.e., the pump power is 40 mW for source I and 42.5 mW for source II in Fig. 1 (d). We find the raw visibilities at 0°/45°/90°/135° in Fig. 5(a) were improved by 9.5%, 9.8%, 10.1% and 8.9% from Fig. 5(a).
The difference of the maximum counts at four different polarizer angles in Fig. 5 might be affected by the relative phase δ in the entangled state . Such a relative phase might be caused by the imperfections of our setup, for example, the spectral mode matching between Hpolarized photons and Vpolarized photons; the slight difference of the quantum efficiency of the four SNSPDs; the splitting ratio of the BS was not exactly 50/50.
All the visibilities in Fig. 5(a, b) are higher than 1/3, verifying the photons are entangled, according to the Peres criteria^{33}. The minimal visibility (V) in Fig. 5(b) is 68.4%, corresponding to a minimal fidelity (F) of 76.3%, by considering the relation 4F = 3V + 1^{13}.
Discussion
Comparison of brightness
We achieved a fourfold coincidence count rate of around 100 cps and a raw (net) visibility of 73.3 ± 1.0% (85.1 ± 0.8%) in the experiment. This count rate is 3 orders higher than the previous experiments at telecom wavelength^{12,13,14,15,16,17,18,34,35}. We compare the brightness of our result with the previous ones at telecom wavelengths in Tab. 2. There are mainly three reasons for this big technical jump in our high fourfold coincidence count rates. The first one attributes to the intrinsic high spectral purity of our source. Thanks to the groupvelocity matching condition, the intrinsics purity is as high as 0.82, which is much higher than the conventional purity of PPLN crystal. Therefore, there is no need for narrow bandpass filters, which are widely used in conventional scheme and decrease the brightness of the source severely. The second reason comes from the optimization of the alignment, especially, the improvement of the coupling efficiency to the single mode fibers for both the clockwise pump and counter clockwise pump in the Sagnacloop. The last and also the most important reason is the high efficiency of our SNSPDs, which showed 30 times higher count rates than the traditional InGaAs avalanche photodiode (APD)^{36}.
Application for field test in free space and fibers
We noticed that our count rates and visibilities are comparable to the previous teleportation and entanglement swapping experiments over 100 km free space channel at ~800 nm wavelengths^{22,23,37}, as compared in Tab. 3. Therefore, our scheme is directly applicable to the longdistance field test of teleportation and entanglement swapping at telecom wavelengths, which is the heart of a global quantum internet^{22,38,39}. Although conventional systems using BBO crystals and SiAPDs are applicable to free space communications, the BBO sources operating at 800 nm band are never applied to fiber communications. With high count rates and visibilities, our source can demonstrate the practical quantum communications using fiber infrastructures. It is also possible to combine both the free space links and fiber links using our scheme. For example, after freespace transmission for a long distance, the photons can be directly collected into fibers for further fiber transmission.
Application for 6, 8photon entangled state
The brightness of our photon source is also comparable to the previous eightphoton entangled state generation experiments at ~800 nm wavelengths^{24,25}, as in Tab. 3. So our source can also be expanded to generate the 6, 8photon entangled state at telecom wavelengths. All the photon sources in Refs. 22,23,24,25, 37 were pumped by the second harmonic of the fundamental Ti:Sapphire lasers operating at ~76 MHz repetition rate. In contrast, our photon source doesn't require a secondharmonic process, which has a limited efficiency. Therefore, our scheme is possible to achieve higher count rate, especially when pumped by highrepetition rate lasers^{40}.
Application for quantum key distribution (QKD)
Our setup opens the way to practical implementation of the qubitamplifier based deviceindependentQKD scheme, which was proposed by Gisin and colleagues in 2010^{41}. Furthermore, our result shows a potential toward the realization of the entanglement swapping based QKD (ESQKD) protocols^{42,43}. In our experiment, we achieved the 4fold CC rate of over 100 cps which could be still meaningful value even in lossy channels. For example, adding a total loss of 10 dB (50 km distance in standard fiber) in our system, the 4fold CC rate remains 10 cps. This is still comparable to the recent field demonstration of the entanglement based QKD in Ref. 44 which suggests that our count rate is enough to realize the first demonstration of the ESQKD.
Application for quantum repeater
In the scenario of quantum repeaters, a point to point quantum communication between remote locations is limited to about 300–500 km due to the losses in fibers, but this problem can be solved by decompose the long distance into serval shorter elementary links. In each link, the entanglement is shared and stored in quantum memories with long coherence time. Finally, the entangled state is retrieved from the quantum memories on demand and swapped between adjacent nodes, so as to faithfully increase the communication distance. Entanglement swapping is the key building block for the construction of quantum repeaters. The recent experimental breakthrough of quantum memory at telecom wavelength has also been reported^{45}. The highly efficient entanglement swapping in this experiment will be an important experimental step toward the realization of quantum repeater protocols.
How to reduce the multipair emission
Multiphoton emission is the main reason for the degradation of raw visibilities in our teleportation and entanglement swapping experiments. To obtain high count rates, we need to excite the SPDC with high pump powers, which inevitably lead to stronger multiphoton emission in SPDC. To solve this problem, recently, we propose and demonstrated a new method  increasing the repetition rate of the pump laser using a 10 GHz repetition rate comb laser^{40}. With such a high repetition rate, we can maintain the high visibilities at high pump powers. Another important limitation of the SPDC source is its intrinsic photon statistics. This could be efficiently circumvented by using a bright SPDC source with recently proposed heralding protocols such as the one in Ref. 46.
Methods
Entangled photon source with GVM condition
Our pulsed polarizationentangled photon source is generated from a periodically poled KTiOPO_{4} (PPKTP) crystal in a Sagnac interferometer configuration. Since the groupvelocitymatching (GVM) condition is satisfied^{47,48}, the intrinsic spectral purity of the photons is much higher than the conventional schemes. Therefore, there is no need to use narrow bandpass filters to improve the spectral purity^{49,50}. The combination of a Sagnac interferometer and the GVMPPKTP crystal makes our entangled source compact, stable, highly entangled, spectrally pure and ultrabright^{19}. The mean photon numbers per pulse are ~0.1 in our photon source with a pump power of ~80 mW. The overall detecting efficiency is ~0.2.
The SNSPDs
Our superconducting nanowire single photon detectors (SNSPDs) have a system detection efficiency (SDE) of around 70% with a dark count rate (DCR) less than 1 kcps^{20,21,36}. The SNSPD also has a wide spectral response range that covers at least from 1470 nm to 1630 nm wavelengths^{36}. The measured timing jitter and dead time (recovery time) were 68 ps^{20} and 40 ns^{51}.
Theoretical prediction of the entangled sources
The theoretical model of the visibility of the polarization correlation (Fig. 2) including multiphoton emissions is established for example in Refs. 28, 52, 53. For the Sagnacloop source with mean photonpair number 2μ and overall efficiency η, the visibility is predicted to be
With 2μ = 0.1 and η = 0.2, we have V = 0.912. Moreover, the model in Ref. 28 can include the imperfection of the PBS (nonzero transmission of the vertically polarized photons). Assuming 1% of unwanted transmittance of vertical photons at the PBSs, the visibility is degraded to be V = 0.876. All the experimental raw visibilities in Fig. 2 are around these values, reflecting the validity of our sources.
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Acknowledgements
The authors thank K. Wakui, M. Fujiwara, T. Yamashita, S. Miki, H. Terai and Z. Wang for helpful discussion and assistance in experiment. R.B. Jin thanks X.H. Bao and H. Jing for valuable suggestions. This work was supported by the Founding Program for WorldLeading Innovative R&D on Science and Technology (FIRST) and Program for Impulsing Paradigm Change through Disruptive Technologies (ImPACT).
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R.J. designed and performed the experiment, collected and analyzed the data and wrote the paper. M.T. constructed a numerical model and analyzed the data. U.T. performed the experiment. R.S. analyzed the data. M.S. supervised the whole project and wrote the paper. All authors contributed to discussion and revision of the manuscript.
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Jin, R., Takeoka, M., Takagi, U. et al. Highly efficient entanglement swapping and teleportation at telecom wavelength. Sci Rep 5, 9333 (2015) doi:10.1038/srep09333
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Physical Review Applied (2019)

Photonic quantum information processing: a review
Reports on Progress in Physics (2019)

Entanglement swapping for generation of heralded timefrequencyentangled photon pairs
Physical Review A (2018)

Highfidelity entanglement swapping and generation of threequbit GHZ state using asynchronous telecom photon pair sources
Scientific Reports (2018)
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