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In this paper we report the generation of wavelength-division-multiplexed, time-bin entangled photon pairs by using cascaded optical second nonlinearities (sum-frequency generation and subsequent spontaneous parametric downconversion) in a periodically poled LiNbO3 device. Visibilities of approximately 94% were clearly observed in two-photon interference experiments for all the wavelength-multiplexed channels under investigation (five pairs), with insensitivity to the polarization states of the photon pairs. We also evaluated the performances in terms of quantum-key-distribution (QKD) applications by using four single-photon detectors, which enables to evaluate the QKD performance properly. The results showed long-term stability over 70 hours, maintaining approximately 3% of the quantum error rate and 110 bit/s of the sifted key rate.
© 2016 Optical Society of America
1. Introduction
Quantum entanglement is peculiar to quantum mechanics, and it necessarily plays an important role in quantum information and communication technology (QICT) applications, including quantum key distribution (QKD) over optical fiber links [1, 2] or in free-space [3, 4] for confidential communications.
The most practical and available source of entangled photon pairs at current status of technologies is based on spontaneous parametric downconversion (SPDC) in a nonlinear optical medium [5–9]. The SPDC-based photon-pair source has been used in many experimental studies concerning QICT applications.
The SPDC-based photon-pair source can be categorized in two, the source with a narrow SPDC spectral bandwidth and the source with a broad spectral bandwidth, from a point of view that whether the application using the generated photon-pairs needs temporal indistinguishability or not. The narrowband source is important for the application that needs indistinguishability (antibunching, quantum repeater [10, 11], et al.,). The SPDC bandwidth of type-II periodically poled LiNbO3 (PPLN) device is typically a few nanometer [8, 12, 13], and this is suitable for this purpose. Spectral slicing technique of a broadband source is also usable for this purpose.
The broadband source implies that its coherence time is very short. This feature is attractive to quantum optical coherence tomography application [14, 15]. Another attractive application of the broadband source is wavelength-division multiplexed (WDM) entanglement distribution combining with spectral slicing technique, which enables multi-user applications [16–18]. In this system, a specific pair of wavelength channels that satisfies the energy conservation law can always share deterministic correlation results, whereas unmatched pairs merely share probabilistic results. This makes many user pairs share different secret keys simultaneously, maintaining security for every user, because one shared key for one user-pair has no correlation with the other shared keys for different user pairs. These features of WDM entanglement distribution with the broadband source will provide more flexible and usable QKD systems in future networks.
In 2013, we have proposed and demonstrated the generation of nearly degenerated WDM polarization entanglement by using cascaded χ(2) processes, sum-frequency generation (SFG) and subsequent SPDC (c-SFG/SPDC), in a single χ(2) device [Fig. 1] [18]. In this double-pumped setup [18, 19], the wavelengths of the pump lights can be set apart from the main spectral lobe of the SPDC spectra, and the main portion of the SPDC spectra, which is totally degenerate, can be freely used as QKD channels. In contrast, in the single-pumped setup using cascaded second-harmonic generation (SHG)/SPDC [9] an intense pump light always exists at the center of the SPDC spectra. The SPDC spectral components near to the wavelength of the pump light cannot be served as the QKD channels, implying that the deadband (typically ~10 nm) always exists at the center of the SPDC spectra in the single-pumped setup. Therefore the double-pumped setup is more suitable to enhance the available bandwidth in WDM system. We have achieved the visibilities higher than 98% in two-photon interference experiments for eight wavelength-pairs in our previous study using cascaded SFG/SPDC method [18].
Fig. 1 Operation principle of (entangled) photon-pair generation by cascaded SFG/SPDC with double-pump scheme. SFG: sum-frequency generation. SPDC: spontaneous parametric downconversion.
Our previous study is based on polarization coding, and therefore entanglement distribution over optical fiber links needs highly accurate control of polarization states of signal and idler photons during fiber transmission. This requirement, however, is not so easy considering current technology status. The other, and the best choice at the current technology level, for long-distance entanglement distribution over optical fiber links is use of time-bin entanglement [20]. This is because the time-bin entanglement is known to be robust to impairment concerning polarization (polarization rotation and polarization-mode dispersion) induced in transmission fibers (of course, as long as the optical devices such as Mach-Zehnder interferometers and single-photon detectors (SPDs) can operate polarization-independently).
In this paper, we report the generation of nearly degenerate, WDM time-bin entangled photon pairs by using c-SFG/SPDC in a PPLN ridge-waveguide device. We observed clear two-photon interference fringes with visibilities of approximately 94% for all the evaluated wavelength channels (five pairs) with insensitivity to the polarization states of the photon pairs. We also evaluated the system performances in terms of QKD application by using four SPDs, in which the sifted key rate and the quantum error rate can be properly evaluated. We have achieves stable distribution of the time-bin entanglement, and hence the quantum keys, over 70 hours, maintaining approximately 3% of the quantum error rate and 110 bit/s of the sifted key rate.
2. Experimental setup
Figure 2 schematically depicts the experimental setup. A home-made PPLN device with a ridge waveguide structure was used as a nonlinear (χ (2)) optical device. The details of the device structure and the fabrication process are available elsewhere [21]. It showed an SHG conversion efficiency of approximately 400%/W under the quasi-phase-matching (QPM) condition. The QPM wavelength (λQPM) was 1550.93 nm at an operating temperature of 28 °C. The PPLN device was packaged in a fiber-pigtailed optical module with a thermistor, a thermoelectric cooler, and two polarization-maintaining optical fibers for standard telecommunication uses. The insertion loss of the module was estimated to be approximately 2.6 dB in the 1.5-μm band.
Fig. 2 Experimental setup. LN mod.: LiNbO3 intensity modulator. EDFA: Erbium-doped fiber amplifier. OBF: optical bandpass filter. WDM: WDM filter. Pol. cntrl.: polarization controller (λ/2 waveplate and λ/4 waveplate). AWG: arrayed waveguide grating module. PLC-MZI: PLC-based Mach-Zehnder interferometer. D1~D4: single photon detectors. TAC: time-amplitude convertor.
The pump lasers were planar external-cavity diode lasers (RIO-ORION modules [22]). One of the pump lights (pump#1) was continuous-wave (CW) light at a wavelength of 1539.77 nm, while the other (pump#2) was pulsed light driven by LiNbO3 intensity modulator. The pulse repetition rate, pulse width, and center wavelength of the pump#2 were 1 GHz, 50 ps, and 1562.26 nm, respectively. The wavelengths of the two pump lasers were set symmetry to the QPM wavelength of the PPLN for efficient SFG.
The pump#2 was amplified by a polarization-maintaining erbium-doped fiber amplifier (EDFA). After narrow-band optical bandpass filters (OBFs, Δλ = 0.8 nm) to eliminate residual amplified spontaneous emission, the two pump lights were coupled to the PPLN module via a WDM filter. The PPLN output first passed a two-stage sharp-edge OBF to eliminate the two pump lights. Figure 3 shows the transmittance curve of the two-stage sharp-edge OBF. The pump rejection ratio was approximately −100.7 dB for the pump#1 (1539.77 nm) and −106.6 dB for the pump#2 (1562.26 nm), respectively. These values were sufficiently low for our experiments.
Fig. 3 Transmittance of two-stage sharp-edge OBF. Red dashed curve: filter#1. Blue dashed curve: filter#2. Black solid curve: total (two-stage).
The output from the sharp-edge OBF was spectrally spliced by an arrayed waveguide grating (AWG) filter. The AWG filter used here was a 10-channel, 50-GHz-spacing AWG filter commonly used in standard telecom applications. Five channels (ch#1–ch#5) in the short-wavelength band corresponded to the signal photons, whereas another five channels (ch#6–ch#10) in the long-wavelength band corresponded to the idler photons. As a result in this work we generated and evaluated five pairs of WDM time-bin entangled photon pairs. Each pair of signal and idler photons was set to satisfy the energy conservation law corresponding to by adjusting the operation temperature of the AWG filter (25.7 °C in this study). Table 1 lists the pair numbers and corresponding AWG filter channel number defined in this work.
Table 1. Definition of pair number and the corresponding channel number of the AWG filter.
The AWG outputs were coupled to silica planar lightwave circuit (PLC)-based Mach-Zehnder interferometers (PLC-MZIs). Polarization controllers consisting of λ/2 and λ/4 waveplates were installed just before the PLC-MZIs to investigate the polarization dependences of the performance.
The constructive and the destructive outputs from the two PLC-MZIs were detected by four InGaAs/InP avalanche photodiode-based SPDs (D1~D4). Owing to a lack of equipment for full setup, the clock (gate) frequency was 40 MHz for D1 and D2 (for detecting the signal photons) while it was 1 GHz for D3 and D4 (for detecting the idler photons). Table 2 lists the performances of the SPDs used in this work. Time tag data of detecting events in each SPD were collected by using time amplitude converters (TACs) and a personal computer, and the coincidence events were calculated. By using the setup above, we could evaluate the sifted key rates and the quantum error rates when the system was applied to the QKD system, although the measurement bases were fixed. In this paper, hits of D1 and D3 were defined as bit = 1, while hits of D2 and D4 were defined as bit = 0.
Table 2. Performances of the SPDs used in this work.
3. Experimental results
3.1 WDM photon-pair generation by cascaded SFG/SPDC process
We first evaluated the characteristics of WDM photon-pairs. We measured the coincidence-to-accidental ratio (CAR) [23] in the time-correlation histogram at the AWG filter output (before the PLC-MZIs), and estimated the distribution of the mean number of the photon pairs (μ) over the pair number of the wavelength-multiplexed channels. The CAR is the ratio of the coincidence counts at delay (τ) = 0 and (τ = 10 ns in this work) in the time-correlation histogram. As discussed theoretically in [23–25], the estimation of the μ from the CAR is insensitive to the optical losses of the optical system and the detection efficiencies of the SPDs when the “true” photon counting rates are sufficiently high and the dark count rates of the SPDs are negligible, whereas the estimation from the photon counting rate of each SPD requires accurate values of the optical loss and the detection efficiency. When the dark counts of the SPDs are negligible the μ can be estimated from the CAR as [23].
Figure 4 show the distribution of the μ over the pair number of the wavelength-multiplexed channels. The averaged powers of the pump lights coupled to the PPLN module were + 4.8 dBm (pump#1) and + 10 dBm (pump#2), respectively. The μ was estimated to be approximately /pulse, and it exhibited almost identical value regardless of the pair number. This indicates that the efficiency of photon-pair excitation was comparable among all the wavelength-multiplexed channels under investigation. The spectral bandwidth of the SPDC was approximately 70 nm (8.7 THz) in full-width at half maximum for the PPLN module used in this work. This implies that a WDM-QKD system consisting of more than 80 independent pairs of WDM channels is possible with this photon-pair source. Further enhancement of the available bandwidth will be possible by optimizing the design of the PPLN waveguide (interaction length, the core size, the clad structure, etc.)
Fig. 4 Dependence of the mean number of photon pairs (μ) on the pair number. The averaged powers of the pump lights were + 4.8 dBm (pump#1) and + 10.0 dBm (pump#2). Error bars showed the maximum and the minimum values at five runs of measurements.
In the entanglement-based QKD system the quantum error rate (QBER) strongly depends on the μ because the multiple photon-pair generation from the SPDC source is the main cause of the QBER [24, 25]. As the μ decreases the QBER, and the sifted key rate, generally decrease. In the case of the time-bin entanglement, the visibility (V) in the two-photon interference and the QBER in the QKD system are roughly related to the μ as [24, 25],
From the μ above (0.0134) we can expect the V and the QBER in this study to be 0.949 and 0.0255, respectively.
3.2 Two-photon interference experiments
We next investigated the time-bin entanglement performances of the wavelength multiplexed channels by measuring the two-photon interference fringes with the PLC-MZIs. In these experiments, we fixed the operating temperature of the PLC-MZI#1 (Tsig,MZI, for signal photons) while changing that of the PLC-MZI#2 (Tid,MZI, for idler photons).
Figure 5 shows the coincidence counts as a function of Tid,MZI for the wavelength pair#1. We undertook several runs of measurements under each condition. Error bars show the maximum and the minimum values for each measurement condition. Circles show the coincidence counts between D1 and D3, while squares are the results of their complements, the coincidence counts between D1 and D4.
Fig. 5 Two-photon interference fringes for the wavelength pair#1. Horizontal scale: chip temperature of PLC-MZI#2 (Tid,MZI) for idler photons. Chip temperatures of PLC-MZI#1 (Tsig,MZI) for signal photons were 55.47 °C (open black circles and red squares) and 55.31 °C (closed blue circles and green squares), respectively. Circles show the coincidence counts between D1 and D3, while squares are the results of their complements, between D1 and D4. Solid curves are fitting curves assuming sine curves.
Open black and red marks show the results when the Tsig,MZI was set at 55.47 °C. Clear two-photon interference fringes were measured. The coincidence counts between D1 and D4 (red squares) were surely complement to those between D1 and D3 (black circles). Almost identical fringes were measured even when the Tsig,MZI, therefore the measurement basis of the signal photons, was changed to 55.31 °C (closed blue and green marks). The visibilities were estimated to be approximately 0.947. This value agreed well with the theoretical prediction (0.949) mentioned above. The peak coincidence counts were approximately 1100 per 20 seconds of the integration time. The single count rates were approximately 1.38 × 10−4 (D1), 1.31 × 10−4 (D2), 1.98 × 10−4 (D3), and 1.99 × 10−4 (D4) per pulse, respectively. They showed almost unchanged values even though the temperatures of the two PLC-MZIs were changed.
Similar two-photon interference fringes were measured for all the measured wavelength-multiplexed channels. Figure 6 summarize the visibilities and the peak coincidence counts for all five wavelength multiplexed channels under investigation in this work. The visibilities were approximately 0.94 for all the measured wavelength-multiplexed channels. The peak coincidence counts showed some uneven. However, this was explained well by the uneven in the optical losses, mainly of the AWG filter, implying that the difference did not originate from the photon-pair source itself.
Fig. 6 Dependences of (a) the visibility and (b) the peak coincidence counts on the pair number in the two-photon interference experiments. Open black circles: results from the coincidence counts between D1 and D3. Open red squares: results from the coincidence counts between D1 and D4.
A main merit of time-bin entanglement for QKD use is robustness to the polarization rotation and polarization-mode dispersion induced in transmission fibers. To investigate the tolerance to the polarization-originated disturbance, we measured the polarization dependence of the performance. In these experiments, the λ/2 and λ/4 waveplates in the polarization controllers set just before the PLC-MZIs were rotated, and the changes in the visibilities and the peak coincidence counts were measured.
Figure 7 summarize the results for the wavelength pair#1. In these experiments the Tsig,MZI and Tid,MZI were fixed at 55.47 °C and 33.86 °C, respectively. The data show the cases: (a), (c) the waveplates at the signal-photon side were fixed, while those at the idler-photon side were rotated. (b), (d) the waveplates at the idler-photon side were fixed, while those at the signal-photon side were rotated. The changes in the visibilities were within 0.93 ± 0.02 (in averaged values per several runs of measurements). This indicates that the change of the QBER is expected to be less than 1% even though the polarization states of incoming signal/idler photon are fluctuated after fiber transmission.
Fig. 7 Results of the polarization dependence of (a), (b) the visibilities and (c), (d) the peak coincidence counts in the two-photon interference fringes for the wavelength pair#1. (a), (c): the polarization states of the idler photons were changed, while those of the signal photons were fixed. (b), (d): the polarization states of the signal photons were changed, while those of the idler photons were fixed. The horizontal scale is the angle of the λ/2 waveplate in the signal/idler side. The angles of the λ/4 waveplate in the signal/idler side were 0° (black), 22.5° (red), 45° (blue), 67.5° (green), and 90° (gray), respectively.
3.3 QKD experiments
Result in Fig. 7 suggests that the system setup in this study has sufficient tolerance to polarization-originated disturbance for long-term operation. Next we investigated the long-term stability. In this session we used all the four SPDs and therefore could evaluate properly the sifted key rate and the QBERs as the QKD system although the measurement bases were fixed.
Figure 8 show the results of the long-term test over 70 hours for the wavelength pair#1. The changes in the sifted key rate and the QBER were sufficiently small, owing to robustness to polarization-originated disturbances. The mean value of the QBER was approximately 2.8% in the case that D1 and D4 were hit, while it was approximately 3.4% in the case that D2 and D3 were hit (Hits of D1 and D3, or D2 and D4, correspond to the cases of correct sifted keys). These values agreed well with the theoretical estimation (0.0255) mentioned above. The number of the shifted keys per round was approximately 1100 bits per each bit. The integration time per round was 20 seconds, and therefore the sifted key rate was estimated to be approximately 110 bit/s in this work.
Fig. 8 Results of long-term test of QKD demonstration for the wavelength pair#1. (a) Number of the sifted keys per round. (b) QBER. Black curves: results from the coincidence events between D1 and D3 or D4. Red curves: results from the coincidence events between D2 and D3 or D4. The integration time per round was 20 seconds.
Figure 9 show the histograms of the error counts for each bit. The distribution agreed well with a Poisson distribution (red curves in the figures), as predicted theoretically. The mean value of the error counts (μe) and the dispersion (σe2) were estimated to be 29.98 and 36.10 in the case that D1 and D4 were hit, and 36.02 and 43.91 in the case that D2 and D3 were hit, respectively, and the relationship μe~σe2 was almost satisfied.
Fig. 9 Histogram of the error counts. (a) signal: bit<1> and idler: bit<0> (D1 and D4 were hit). (a) signal: bit<0> and idler: bit<1> (D2 and D3 were hit). Red solid curves were fitting curves assuming a Poisson distribution.
Similar experiments for evaluating the long-term stability were performed for different wavelength-pair (pair#5). The results of the QBER were shown in Fig. 10. In these experiments, the operating temperatures of the PLC-MZIs were changed (Tsig,MZI = 51.23 °C and Tid,MZI = 38.38 °C, respectively) in order to maintain sufficiently small dependence on the polarization. Actually the optimum operation temperature of the PLC-MZI for the polarization-independent operation depended on the wavelength. Experimentally in this study, the dependence of the optimum operating temperature on the wavelength had a slope of roughly 2.7 °C/nm.
The changes in the QBER for the wavelength pair#5 were sufficiently small, as in the case of Fig. 8. The mean values were estimated to be 3.1% (black curve) and 2.7% (red curve), respectively. These values were comparable to those of the case of the pair#1 (see Fig. 8), indicating that similar performances as QKD system can be expected among different wavelength-multiplexed channels in this system.
By using a similar setup, we also tested the performances of the polarization coding (polarization entanglement). The results showed drastic, and frequently rapid, changes in the QBER, within a few minutes at the worst case. This was owing to the change in the environment temperature in our laboratory room. This difference verifies the merit of the time-bin entanglement for stable QKD operation in practical system.
4. Conclusion
In summary we report the generation of nearly degenerate, WDM time-bin entangled photon pairs by using c-SFG/SPDC in a PPLN device, aiming at multiple user-pair installation in constructing more flexible QKD network. We have achieved visibilities of approximately 94% in the two-photon interference experiments for all the evaluated wavelength channels (five pairs), with insensitivity to the polarization states of the photon pairs. The results were applied to QKD demonstration by using four SPDs, in which the sifted key rate and the QBER could be properly evaluated. We have achieved stable distribution of the entanglement, and hence the quantum keys, over 70 hours, maintaining approximately 3% of the QBER and 110 bit/s of the sifted key rate during the measurements. Stable long-term operation was also ensured in different wavelength-multiplexed channels. Considering the bandwidth of the SPDC spectra (approximately 70 nm in this study), a WDM-QKD system consisting of more than 80 independent pairs of wavelength-multiplexed channels is possible with this photon-pair source, with sufficient insensitivity to the polarization-originated disturbance in the optical fiber links.
References and links
1. C. Liang, K. F. Lee, J. Chen, and P. Kumar, “Distribution of fiber-generated polarization entangled photon-pairs over 100 km of standard fiber in OC-192 WDM environment,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2006), paper PDP35.
2. J. F. Dynes, H. Takesue, Z. L. Yuan, A. W. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17(14), 11440–11449 (2009). [CrossRef] [PubMed]
3. K. Resch, M. Lindenthal, B. Blauensteiner, H. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city, free-space quantum channel,” Opt. Express 13(1), 202–209 (2005). [CrossRef] [PubMed]
4. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 (2007). [CrossRef]
5. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995). [CrossRef] [PubMed]
6. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultra-bright source of polarization-entangled photons,” Phys. Rev. A 60(2), R773–R776 (1999). [CrossRef]
7. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarization-entangled photon pairs at 1550 nm using two PPLN waveguides,” Electron. Lett. 39(7), 621–622 (2003). [CrossRef]
8. A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-II PPLN waveguide emitting at a telecom wavelength,” New J. Phys. 12(10), 103005 (2010). [CrossRef]
9. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ2 processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]
10. J.-W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80(18), 3891–3894 (1998). [CrossRef]
11. H. de Riedmatten, I. Marcikic, J. A. W. van Houwelingen, W. Tittel, H. Zbinden, and N. Gisin, “Long distance entanglement swapping with photons from separated sources,” Phys. Rev. A 71(5), 050302 (2005). [CrossRef]
12. G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15(20), 12769–12776 (2007). [CrossRef] [PubMed]
13. T. Suhara, H. Okabe, and M. Fujimura, “Generation of polarization-entangled photons by type-II quasi-phase-matched waveguide nonlinear-optic device,” IEEE Photonics Technol. Lett. 19(14), 1093–1095 (2007). [CrossRef]
14. A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum optical coherence tomography with dispersion cancellation,” Phys. Rev. A 65(5), 053817 (2002). [CrossRef]
15. M. Okano, H. H. Lim, R. Okamoto, N. Nishizawa, S. Kurimura, and S. Takeuchi, “0.54 μm resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography,” Sci. Rep. 5, 18042 (2015). [CrossRef] [PubMed]
16. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Broadband source of telecom-band polarization-entangled photon-pairs for wavelength-multiplexed entanglement distribution,” Opt. Express 16(20), 16052–16057 (2008). [CrossRef] [PubMed]
17. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Wavelength-multiplexed distribution of highly entangled photon-pairs over optical fiber,” Opt. Express 16(26), 22099–22104 (2008). [CrossRef] [PubMed]
18. S. Arahira and H. Murai, “Nearly degenerate wavelength-multiplexed polarization entanglement by cascaded optical nonlinearities in a PPLN ridge waveguide device,” Opt. Express 21(6), 7841–7850 (2013). [CrossRef] [PubMed]
19. M. Medic, J. B. Altepeter, M. A. Hall, M. Patel, and P. Kumar, “Fiber-based telecommunication-band source of degenerate entangled photons,” Opt. Lett. 35(6), 802–804 (2010). [CrossRef] [PubMed]
20. J. Brendel, W. Tittel, H. Zbinden, and N. Gisin, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999). [CrossRef]
21. T. Kishimoto and K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO3 wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photonics Technol. Lett. 23(3), 161–163 (2011). [CrossRef]
22. Redfern Integrated Optics Inc, http://www.rio-inc.com/ (California, USA).
23. H. Takesue and K. Inoue, “1.5-microm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13(20), 7832–7839 (2005). [CrossRef] [PubMed]
24. B. Miquel and H. Takesue, “Observation of 1.5μm band entanglement using single photon detectors based on sinusoidally gated InGaAs/InP avalanche photodiodes,” New J. Phys. 11(4), 045006 (2009). [CrossRef]
25. S. Arahira and H. Murai, “Effects of afterpulse events on performance of entanglement-based quantum key distribution system,” Jpn. J. Appl. Phys. 55(3), 032801 (2016). [CrossRef]
