1. Introduction

Quantum entanglement is not explained by the laws of classical physics and peculiar to quantum mechanics. The quantum entangled particles can make two distant observers share the results with nonlocal correlations. One of the promising and attractive applications using the quantum entanglement is quantum key distribution (QKD) for confidential communications with unconditionally security based on the laws of the quantum mechanics.

To realize the quantum-entanglement-based communication networks, distribution of the quantum entanglement over long distance is necessary. The photon-based quantum entanglement is the most promising solution for this purpose. Distribution over the optical fiber links has a merit that the quantum communication networks can be constructed by using the existing worldwide telecommunication infrastructure and optical resources. Utilizing installed telecom dark optical fiber links will provide both a practical and cost-effective quantum communications for real uses. A lot of demonstrations concerning the long-distance distribution of the quantum entanglement have been performed over the optical fibers in which at least one photon in the 1.5-μm telecom band is used [1–8]. The long-distance distribution has been also reported in free-space links [9, 10]. The free-space links are promising, especially for distribution of the polarization entanglement, because of birefringent and polarization-mode dispersion (PMD)-free transmission performance.

To our knowledge, the best value in terms of transmission distance of the quantum-entanglement distribution reported so far is 200 km, or 42 dB of the total transmission loss, over the dispersion-shifted optical fibers (DSFs) by using a periodically poled LiNbO₃ (PPLN) device and InGaAs avalanche photodiodes (APDs) in a self-differencing mode [7].

The maximum reach of the distribution of the quantum entanglement is mainly determined by the following parameters: optical loss in the transmission media (typically 0.2 dB/km at 1.5-μm band in optical fibers), dark counts and detection efficiencies of single photon detectors (SPDs), optical loss in the entangled photon-pair source, the probability of the multi-photon-pair generation, and the probability of the noise photons mainly due to the Raman scattering generated from the photon-pair source itself and also from the transmission lines.

Among them, the photon-pair source and the single photon detector are vital components which give actual limit to expand the distribution distance. They should be highly pure with, at the least from the point of the views of practical uses, negligible noise photons and dark counts. Simultaneously they should be as practical as possible in terms of the cost, the reliability, and the compatibility with the existing systems. The results in Ref [7]. indicate that inexpensive InGaAs APDs are usable as the practical SPDs for distribution distance of 200 km if they are managed in a suitable design.

As for the photon-pair source, the photon-pair source based on spontaneous parametric down conversion (SPDC) is almost noise-photon-free because the Raman-induced photons are generated in the wavelength band far away from the photon-pairs and they can be easily eliminated. Mainly for this reason, the SPDC-based sources are used in most of the experimental demonstration of the long-distance distribution of the quantum entanglement. While the SPDC process is a powerful and usable tool, it often requires a complicated optical coupling system. This is because the photons at quite different wavelengths (short-wavelength pump photon and long-wavelength photon-pair) should be simultaneously managed.

In contrast, optical fiber-based photon-pair source often has serious impairments due to considerable Raman-induced photons [11, 12], even though it has a merit that the source can entirely consist of the telecom-compatible optical resources.

Recently a new type of the quantum-entangled photon-pair source by using cascaded χ⁽²⁾ processes, the second harmonic generation (SHG) and the following SPDC (c-SHG/SPDC process), was reported by some research groups including us [13–15]. We revealed that this photon-pair source using a periodically poled LiNbO₃ (PPLN) ridge-waveguide device had very low contribution of the Raman noise photons, even though the pump photon, the Raman photon, and the photon-pairs are in the same wavelength-band [14, 15]. The photon-pair source can also consist of the optical resources used in the standard telecom fields. This leads to the realization of low-cost and reliable photon-pair source. But detailed investigation in transmission performance of the quantum entanglement using this photon-pair source has not been reported to date.

In this paper we report the experimental studies in transmission performance of the polarization-entangled photon-pairs generated by the c-SHG/SPDC in a PPLN ridge-waveguide device over the standard single-mode optical fibers (SMFs). We observed clear two-photon interference fringes even after the transmission over 140 km of the SMF spools. The degradation in the visibility was less than 3% (approximately from 91% to 88%) even after the fiber transmission. This value agreed well with theoretical assumption. The results indicate that the QKD systems with the c-SHG/SPDC-based entangled photon-pair source can fully cover metro/access networks in which the standard SMFs are used without dispersion management. We also tested the performance by using optical attenuators, instead of the SMF spools, to study the maximum reach of the distribution in terms of loss penalty. The results revealed that the visibility exceeding 70.7% could be obtained even with 25 dB of the single channel loss, indicating that the quantum entanglement with the violation of the Bell inequality could be retained even at 50 dB of the transmission loss by using the c-SHG/SPDC-based entangled photon-pair source with proper dispersion management.

2. Experimental setup

Figure 1 schematically draws the experimental setup. Setup of the polarization-entangled photon-pair source was detailed in our preceding work [14]. The home-made PPLN device with a ridge-waveguide structure was used in this work. It showed approximately 700%/W of the SHG conversion efficiency under the QPM condition at 1548.6 nm of the pump wavelength. The PPLN device was then packaged in a fiber-pigtailed optical module with a thermistor, a thermoelectric cooler, and two polarization-maintaining optical fibers (PMFs) for standard telecommunication uses. The insertion loss of the module was estimated to be approximately 3.0 dB at the 1.5-μm band.

 

Fig. 1 Experimental setup. PBSC: polarization beam splitter/combiner. OPBC: optical phase-bias compensator. PC: polarization controller. Pol.: rotatable fiber polarizer.

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The pump pulses were generated using a wavelength-tunable external-cavity laser diode and a LiNbO₃ intensity modulator. The pulse repetition rate, the pulse width, and the center wavelength of the pump pulses were 240 MHz, 120 ps, and 1548.66 nm (corresponding to the QPM wavelength), respectively. After amplification by a polarization-maintaining erbium-doped fiber amplifier (PM-EDFA), residual amplified spontaneous emission (ASE) was eliminated by using a narrow-band optical bandpass filter (OBF#1). The 45 ° -polarized pump pulses then passed a WDM filter (WDM#1) and a polarization beam splitter/combiner (PBSC), and finally excited the PPLN module bidirectionally.

Since strong pump light remains at the center of the SPDC spectra in the c-SHG/SPDC based system, the pump light should be sufficiently reduced and the generated photon-pairs should be wavelength non-degenerate in the c-SHG/SPDC based system. The signal and the idler photons by the c-SHG/SPDC from the fiber loop passed the optical filtering system consisting of an optical low pass filter (LPF) and three-step WDM filters (WDM#1, #2, and #3). The LPF, the WDM#1, and the WDM#2 were mainly used to eliminate the pump light and the SHG light. Then the signal/idler photons were spatially separated by WDM#3 and two optical bandpass filters (OBF#2 and OBF#3). In this work we set the center wavelengths of the signal photons and the idler photons to 1538.8 nm and 1558.66 nm, respectively. Wavelength detuning from the pump wavelength was approximately 10 nm. The peak transmittance was −9.4 dB for the signal photons and −7.9 dB for the idler photons, respectively, including the insertion losses of the polarization controllers (PCs) and the rotatable polarizers to evaluate the two-photon interference fringes. The 3-dB bandwidth of the transmittance window was approximately 0.6 nm for the signal photons and 0.67 nm for the idler photons, respectively.

The photon-pairs were then launched into two individual transmission lines. In this work, we used two types of the transmission lines (Fig. 2 ). One was two standard SMF reels combined with optical circulators (OCRs) and Faraday rotator mirrors (FRMs) (Fig. 2 (a)), and another was variable optical attenuators (Fig. 2 (b)).

 

Fig. 2 Transmission lines used in this study. (A) transmission over SMF reel. (B) transmission with variable optical attenuator.

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In this work we used the standard SMFs as the transmission lines, while dispersion-shifted fibers (DSFs) or non-zero dispersion shifted fibers (NZ-DSF) has been commonly used in the long-distance QKD experiments [2–8] to avoid or reduce the pulse broadening due to the chromatic dispersion (CD). But such fibers are actually used in backbone (core) networks for very long-distance transmission (>1000 km) in the existing optical telecommunication infrastructure. Considering the present technical status of the QKD system, a realistic target at the first step of the QKD system should be the realization of the QKD networks over metro/access networks in which the standard SMFs are commonly installed without dispersion management. For this purpose the evaluation in the transmission performance over the standard SMF infrastructure is strongly desired.

Different from the time-bin entanglement protocol [2, 4, 5, 7], the performance of the polarization entanglement is strongly dependent on the state-of-polarization (SOP) of the photon-pairs after the distribution. The SOP of the photon-pairs after the fiber transmission is in general remarkably fluctuated, therefore any polarization control scheme is necessary for actual long-distance distribution [3, 8]. In the setup of Fig. 2(a), the change of the SOP in the long SMF reel was almost compensated due to polarization-exchange by the FRM located at the center of the transmission line. This setup quite resembles “Plug-and-Play” system for BB84 protocol [16], but is maybe not suitable to actual system of the distribution of the quantum entanglement. This is because in this setup the photons should roundtrip between two distant observers and doubled transmission loss will seriously degrade the transmission performance. Consequently this setup is used only in laboratory for the experimental convenience, but is effective and usable to estimate the performance in the long-distance distribution over the true transmission line. The insertion loss of the OCR and the FRM was approximately 2.2 dB in this study. The transmission loss of the SMF reel was typically 0.21 dB/km.

The setup using the variable optical attenuators is usable to estimate the maximum reach of the distribution when the transmission performance is simply dominated by the optical losses. This setup also almost corresponds to the case of the distribution over the DSFs.

Monitor light coupled to the Sagnac loop of the photon-pair source via a 1:9 coupler was used to monitor the polarization rotation during the fiber transmission and to compensate it by the polarization controllers (PCs).

The signal/idler photons were finally detected by using InGaAs-APD based single photon detectors (Princeton lightwave benchtop receiver PGA-600HSU) (D1, D2). Periodical gate voltages applied to the two APDs were synchronized to the pump pulses. The gate frequency was 40 MHz. The detection efficiencies of both the APDs were estimated to be approximately 20%. The gate width was 1 ns. The dark count rates were approximately 2x10⁻⁶ per pulse for both detectors.

3. Experimental entanglement distribution

3.1Distribution over the SMF reels

We investigated the performance of the long-distance distributions by measuring two-photon interference fringes. In these measurements, we fixed the polarizer angle of the signal polarizer (θ_s), and measured the coincidence counts while rotating the polarizer angle of the idler polarizer (θ_i). The averaged pump power (P_ave) was approximately −2.1 dBm per end facet of the PPLN module (totally + 0.9 dBm for both facets). The pulse peak power was estimated to be + 12.9 dBm from the experimental conditions. This value almost corresponded to the condition in which the mean number of the photon-pair per pulse (μ_c) was 0.1. While the optimal value of the μ_c which maximizes the final secure key rate after distillation is slightly changed depending on security scenario, 0.1 of the μ_c almost corresponds to the optimal value in most cases [17]. A smaller μ_c will increase the visibility, and therefore decrease the quantum error rate, in our setup.

The optical phase difference in the optical phase bias compensator (OPBC) [14] of the photon-pair source was adjusted so that the coincidence counts were minimized when θ_s = + 45° and θ_i = −45°. This implies that the quantum state used here was adjusted to be $1/\sqrt{2}\left({|H〉}_s{|H〉}_i+{|V〉}_s{|V〉}_i\right)$state. The setting value of the OPBC remained constant during each measurement of the two-photon interference fringe. This value was slightly adjusted again when the SMF reels was changed, because of the residual birefringence of the SMF reels. All the data were raw data without subtracting the accidental counts. We undertook several runs of the measurements at specific conditions in which the coincidence counts were maximized and minimized, i. e., θ_s = 0° and θ_i = 0° and 90° in the H/V basis; θ_s = + 45° and θ_i = + 45° and −45° in the diagonal basis, to estimate standard deviation and error bars of the measurements.

Figure 3 show the coincidence counts as a function of θ_i at the H/V basis and the diagonal basis (θ_s = 0° and + 45°, respectively) after the distribution over the SMF reels. Before the fiber transmission (Fig. 3(a)), the visibilities of the fitted curves were estimated to be 91.4 ± 0.5% in the H/V basis (θ_s = 0°) and 91.2 ± 2.1% in the diagonal basis (θ_s = + 45°). The peak coincidence counts were approximately 4000 counts/15 seconds for both the H/V basis and the diagonal basis. The single count rate was approximately 5.1x10⁻⁴ per pulse and 6.3x10⁻⁴ per pulse for the signal photons and the idler photons, respectively.

 

Fig. 3 Two-photon interference fringes after (a) 0 km (back-to-back), (b) 40 km, and (c) 140 km transmission over the SMF fiber reels. Black closed circles: results of the H/V basis. Red closed circles: results of the diagonal basis. Polarizer angle of the signal polarizer (θ_s) were 0° (H/V basis) and + 45° (diagonal basis), respectively. The solid curves in the figures are fitting curves assuming${\cos }^2\left({\theta }_s-{\theta }_i\right)$.

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The ratio between the coincidence count rate and the single count rate for the signal (idler) photons gives the channel loss for the idler (signal) before transmission (see [14] for details). The μ_c can be also estimated from the single count rate and the channel loss.

From experimental values above, we estimated the channel loss before the transmission to be 19.8 dB (α_s) and 18.8 dB (α_i), respectively, for the signal photons and the idler photons. These values included the detection efficiencies of the SPDs and the insertion losses of the polarization controllers and the fiber polarizers as well as the transmission losses of the optical filters. Also from these values, the μ_c was experimentally determined to be 0.096. This value agreed well with the visibilities in the two-photon interferences. The pump rate of the photon-pair source, hence the μ_c, remained the same during all the distribution experiments hereafter.

Figure 3(b) and 3(c) show the results after the fiber transmission. The visibilities in the two-photon interferences exhibited no significant changes when the distribution length was less than 100 km (50 km x 2), even though the coincidence count rate was decreased corresponding to the increase of the loss. After the 140-km transmission (70 km x 2) (Fig. 3(c)), the visibilities were estimated to be 88.7 ± 4.7% in the H/V basis (θ_s = 0°) and 88.2 ± 3.9% in the diagonal basis (θ_s = 45°). The decreases in the visibilities agreed well with the theoretical assumption, as is discussed in detail in Section 3.3. These results indicate that the QKD system consisting of the c-SHG/SPDC-based photon-pair source and the inexpensive InGaAs-APD-based detectors can fully cover the SMF-based metro/access networks, at least in terms of the security of the confidential communications.

In this work, further expanding of the distribution distance was limited by the temporal broadening of the wave packet of the photon-pairs due to the CD. The CD of the SMF in the 1.5-μm band is typically 18 ps/km/nm. The pulse width after the fiber transmission is approximately given by $CD•\Delta \lambda •L$, where Δλ is the spectral bandwidth of the signal/idler photons and L is the SMF length. Since the Δλ was approximately 0.65 nm in this work, the pulse width was broadened to approximately 1.2 ns after the transmission over 100 km of the SMF. This value was comparable to the gate width of the SPD in this work (1 ns), and showed remarkable influence on the performance of the distribution, especially on the coincidence counts. This was discussed in more detail in Section 3.3.

3.2 Distribution over the optical attenuators

Experiments with the variable optical attenuators, instead of the SMF reels, are usable to estimate the final performance of the long-distance distribution if the transmission performance is only limited by the transmission loss without the other transmission impairments such as the CD, the PMD, and the SOP fluctuations.

Figure 4 show the results of the two-photon interference fringes, as a function of single channel loss for the signal/idler photons. We observed clear two-photon interference even after giving 25 dB of the single channel loss (total loss was 50 dB). The visibilities were estimated to be 79.9 ± 7.9% in the H/V basis and 79.4 ± 7.7% in the diagonal basis at 22.5 dB of the single channel loss, whereas they were 74.0 ± 10.7% in the H/V basis and 74.2 ± 9.5%, respectively at 25 dB of the single channel loss. The results indicate that the Bell inequality might be violated by a standard deviation in the case of 22.5 dB of the single channel loss. They also strongly suggest that the violation of the Bell inequality was still retained even with 25 dB of the single channel loss. This indicates that our simple setup consisting of the telecom-compatible optical resources can distribute the quantum entanglement over 250 km of the optical fibers.

 

Fig. 4 Two-photon interference fringes when additional losses were given by the optical attenuators. (a) −8 dB/channel. (b) −18 dB/channel. (c) −25 dB/channel. Black closed circles: results of the H/V basis. Red closed circles: results of the diagonal basis. Polarizer angle of the signal polarizer (θ_s) were 0° (H/V basis) and + 45° (diagonal basis), respectively. The solid curves in the figures are fitting curves assuming ${\cos }^2\left({\theta }_s-{\theta }_i\right)$.

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3.3 Discussion on the experimental results

Figure 5 shows the summary of the visibilities in the two-photon interference fringes as a function of the single channel loss. The results using the SMF reels are shown as open circles, whereas those using the optical attenuators are shown as open triangles.

 

Fig. 5 Dependence of the visibilities in the two-photon interference fringes on the single channel loss. Circles: experimental results with the SMF fiber reels. Triangles: experimental results with the optical attenuators. Black solid curve: calculation results using Eq. (1). Black dashed curve: calculation including the pulse broadening due to the CD. Results in Ref [7]. were also shown as gray squares for comparison.

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Assuming Poisson distribution as photon-number statics, the visibility in the two-photon interference of the polarization entanglement, V, is given by [18],

Solid curve in Fig. 5 shows the calculation from Eq. (1) using the experimental parameters given in the earlier sections. Here the s_nx was ignored. The experimental results agreed well with theoretical values. This implies that in the c-SHG/SPDC-based photon-pair source the noise photons such as the Raman scattering showed negligible influence on the performance of the long-distance distribution and that the theoretically expected performance was well realized.

The results imply both theoretically and experimentally that the quantum entanglement in this work could violate the Bell inequality (V>70.7%) even when the single channel loss was 25 dB. In terms of the secure communication, theoretical assumption indicates that the final distilled secret keys can be obtained if the quantum error rate is below approximately 11.4% [17]. The error rate corresponds to approximately 77.2% of the visibility. Our results also show that the secure communication is possible over 225 km of the SMF transmission lines (22.5 dB in the single channel loss).

In Fig. 5, the results in Ref [7] are also shown as gray squares for comparison. Our results exhibited better values than those in Ref [7] both theoretically and experimentally. While the differences of course reflected the differences in the experimental setup (detection efficiencies, losses, and etc.), we can point out that they also originate from the fundamental predominance of the polarization-entanglement over the time-bin entanglement.

In the time-bin entanglement, the “true” coincidence count rate becomes half of that of the polarization-entanglement in principle, while the accidental count rate is the same, if the μ_c is the same. This implies that the visibility is worse in the time-bin entanglement than in the polarization entanglement.

Figure 6 shows the summary of the coincidence count rates at the matched time slot. The coincidence count rate at the matched time slot is given by,

 

Fig. 6 Dependence of the coincidence count rates on the single channel loss. Black closed circles: experimental results with the SMF fiber reels. Red closed circles: experimental results with the optical attenuators. Solid curve: calculation results only considering optical losses. Dashed curve: calculation results considering both the optical losses and the pulse broadening due to the chromatic dispersion (CD) of the SMF.

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The results using the optical attenuators agreed well with the theoretical curve shown as the black thin curve. In contrast the results using the SMF reels showed smaller coincidence count rates as the loss per channel, therefore the transmission distance, increased.

Taking into account the pulse broadening due to the CD after the fiber transmission, the channel loss η_x should be expressed as,

Dashed curves in Fig. 6 show the calculation results including the effect of the pulse broadening. The calculation results agreed well with the experimental ones in the SMF reels.

Black dashed curves in Fig. 5 show the calculation results of the visibilities considering the pulse broadening effect by the CD. In this case the visibility degraded less than 80% even with 20 dB of the single channel loss. This implies that additional loss by the pulse broadening effect given by Eq. (3) is also a parameter to limit the maximum reach of the quantum entanglement distribution. This also indicates that the entanglement distribution over 250 km of the optical fiber links is possible with proper dispersion management, such as by using the DSFs, the NZ-DSFs, and the dispersion compensating fibers (DCFs), by using this photon-pair source. The reduction of the CD effect is also possible by narrowing the bandwidth of the optical filters to extract the photon-pairs, as well as by broadening the gate width of the SPDs.

In the true transmission lines in the fields, the polarization-mode dispersion (PMD) of the optical fibers should be another vital parameter that determines the maximum reach of the distribution. The PMD induces remarkable decoherence and would give the final limit of the possible distribution distance, even when the CD, the SOP fluctuation, and the other transmission impairments are perfectly controlled. The effect of the PMD has been discussed in some preceding papers including Ref [3, 8]. The PMD value is known to range 0.2 ps/$\sqrt{km}$ to 1 ps/$\sqrt{km}$ for installed old fibers and is improved to less than 0.1 ps/$\sqrt{km}$ in recent fibers. Considering this, to speak properly, the PMD effect might affect to some degrees the performance of the entanglement distribution, especially for the 140-km transmission, over “true” transmission lines, since the coherent time of the photon-pairs was estimated to be approximately 6 ps from the filter bandwidth (0.6 nm) in this work. A simple and promising way to relax the PMD issue is narrowing the bandwidth of the optical filters to extract the photon-pairs, as is the case of the relaxation of the pulse broadening due to the CD. Typical bandwidth of the arrayed waveguide filter (AWG) commonly used in WDM systems in classical communications is 0.2 nm, and use of this will improve the tolerance to the PMD issue, by three times in comparison with the setup in this paper.

4. Conclusion

In summary we have reported experimental investigation in the transmission performance over standard SMFs of the polarization-entangled photon-pairs generated by the c-SHG/SPDC in a PPLN ridge-waveguide device. Clear two-photon interference fringes have been observed after the distribution of 140 km of the SMF fiber spools with approximately 88% of the visibilities. The degradation in the visibility was less than 3% even after the fiber transmission. This revealed that the QKD systems with this entangled photon-pair source could fully cover metro/access networks consisting of the standard SMFs without dispersion management. Demonstration using the optical attenuators revealed that the quantum entanglement could remain even at 50 dB of the transmission loss with the violation of the Bell inequality and also that secure communication was possible even at 45 dB of the transmission loss. These results indicate that the c-SHG/SPDC-based photon-pair source can offer the long-distance QKD networks over the preinstalled telecom infrastructure using the SMFs.