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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 29013–29024
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Demonstration of active routing of entanglement in a multi-user network

I. Herbauts, B. Blauensteiner, A. Poppe, T. Jennewein, and H. Hübel  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 29013-29024 (2013)
http://dx.doi.org/10.1364/OE.21.029013


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Abstract

We implement an entanglement distribution network based on wavelength-multiplexing and optical switching for quantum communication applications. Using a high-brightness source based on spontaneous parametric down-conversion in periodically-poled lithium niobate waveguides, we generate polarisation entangled photon pairs with a broad spectrum covering the telecom wavelengths around 1550 nm. The photon pairs have entanglement fidelities up to 99%, and are distributed via passive wavelength multiplexing in a static multi-user network. We furthermore demonstrate a possible network application in a scenario with a single centralised source dynamically allocating two-party entanglement to any pair of users by means of optical switches. The whole system, from the pump laser up to the receivers, is fibre and waveguide based, resulting in maximal stability, minimal losses and the advantage of readily integrable telecom components in the 1550 nm range.

© 2013 OSA

1. Introduction

Quantum entanglement is an essential resource for many quantum information experiments, such as quantum teleportation, entanglement swapping and tests of Bell inequalities [1

1. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012). [CrossRef]

]. It is also useful in quantum communication protocols such as Quantum Key Distribution (QKD) [2

2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]

]. For QKD in particular, entanglement offers the additional advantage of device independent security [3

3. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007). [CrossRef] [PubMed]

]. Entanglement-based QKD is now a well developed research area which has, in the last years, reached important practical milestones [4

4. T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. H. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over optical fiber,” Opt. Express 16, 19118–19126 (2008). [CrossRef]

7

7. M. P. Peloso, I. Gerhardt, C. Ho, A. Lamas-Linares, and C. Kurtsiefer, “Daylight operation of a free space, entanglement-based quantum key distribution system,” New J. Phys. 11, 045007 (2009). [CrossRef]

]. Forefront developments in the field include also the realisation of more sophisticated multi-party QKD networks [8

8. M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fuerst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Laenger, M. Legre, R. Lieger, J. Lodewyck, T. Loruenser, N. Luetkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009). [CrossRef]

,9

9. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legre, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Laenger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19, 10387–10409 (2011). [CrossRef] [PubMed]

], with trusted nodes connecting different independent QKD-links. So far however, only photonic qubits were distributed in these demonstrations, but no entanglement. The realisation of entanglement-distribution networks connecting multiple users sharing entanglement would permit a wide variety of quantum communication applications in addition to QKD such as secret key sharing [10

10. M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999). [CrossRef]

] and quantum complexity protocols [11

11. H. Buhrman, R. Cleve, and W. Van Dam, “Quantum entanglement and communication complexity,” Siam Journal on Computing 30, 1829–1841 (2001). [CrossRef]

].

Entangled photon sources (EPS) used in such networks should incorporate design features to integrate them easily into the existing telecommunication infrastructure. It is therefore advantageous to have compact, cheap and power-saving systems which are also compatible with fibre-based telecom components. For practical ground-based networks, the generation of entangled photons around 1550 nm is beneficial, since long distance transmission in fibre is optimal at that wavelength and there exist standardised grids in the form of Dense Wavelength Division Multiplexing (DWDM) and Coarse Wavelength Division Multiplexing (CWDM) [12

12. ITU-T recommendation G.694.2 (2003).

].

A common technique to create and make practical use of entanglement is to produce polarization-entangled photons by spontaneous parametric down-conversion (SPDC) in second order (χ2) non-linear crystals [13

13. 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, 4337–4341 (1995). [CrossRef] [PubMed]

]. The coupling of photons from the bulk crystal to optical fibres leads to a loss of robustness and reliability, both needed in practical applications. Non-linear crystals with inscribed waveguides and fibre pigtails overcome this problem and offer long term stability. In addition, waveguides also increase the efficiency of the down-conversion process by several orders of magnitude compared to bulk crystals [14

14. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electronics Lett. 37, 26–28 (2001). [CrossRef]

]. Entangled photon pairs have also been directly generated in dispersion shifted fibres via four-wave mixing techniques (χ3) [15

15. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Express 31, 1905–1907 (2006).

]. Such designs offer the advantage of an all-fibre based compact system with no coupling losses from crystal to fibre. The χ3 process however suffers from Raman scattering, leading to an increase in background photons. To limit the scattering, fibres have to be cooled with liquid nitrogen or the produced photon pair has to lie outside the scattering band (Δλ ∼ 250 nm) [16

16. S. X. Wang and G. S. Kanter, “Robust multiwavelength all-fiber source of polarization-entangled photons with built-in analyzer alignment signal,” IEEE Journal of selected topics in quantum electronics 15, 1733–1740 (2009). [CrossRef]

18

18. E. Meyer-Scott, V. Roy, J.-P. Bourgoin, B. L. Higgins, L. K. Shalm, and T. Jennewein, “Generating polarization-entangled photon pairs using cross-spliced birefringent fibers,” Opt. Express 21, 6205–6212 (2012). [CrossRef]

]. Neither option is very practical for realistic telecom applications since cooling requires more maintenance and larger source designs, or the photons would lie outside the telecommunication band (1260–1675 nm), due to the large wavelength separation. Recent developments include the generation of entangled photon pairs in a twin-hole step-index fibre via χ2 nonlinearities [19

19. E. Y. Zhu, Z. Tang, L. Qian, L. G. Helt, M. Liscidini, J. E. Sipe, C. Corbari, A. Canagasabey, M. Ibsen, and P. G. Kazansky, “Direct generation of polarization-entangled photon pairs in a poled fiber,” Phys. Rev. Lett. 108(2012). [CrossRef]

]. Although this seems a promising way for the future, conversion efficiencies of χ2-fibres are currently still much lower than in χ2-crystals with waveguides which are the best candidates for practical realisations.

Fig. 1 Outline of an entanglement distribution network. Each user is connected via a single quantum channel (solid lines) to the centralised entangled-photon-source (EPS). Entanglement (dotted arrows), used for quantum information tasks, can be shared between any two users on request (only certain combinations are shown).

In Section 2, we describe in detail the experimental setup, comprising the source, the implementation of active phase-stabilisation, the components designed for multi-user entanglement distribution, the polarisation analysis as well as the detection modules. We present, in Section 3, the key performance parameters (coincidence rates and conversion efficiency), as well as the results of tomographic measurements on the entangled channels. With the introduction of optical switches we demonstrate in Section 4 a “any Alice to any Bob” 4-user SDN application for entanglement distribution, before concluding in Section 5.

2. Setup

2.1. Source of polarisation entangled photons

The source, depicted in Fig. 2, is based on two 30 mm long, periodically poled LiNbO3 crystals (ppLN) arranged in a Mach-Zehnder interferometer to yield polarisation entanglement [21

21. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarisation-entangled photon pairs at 1500 nm using two PPLN waveguides,” Electronics Lett. 39, 621–622 (2003). [CrossRef]

]. The crystals are type-0 quasi phase-matched (all interacting fields have the same polarisation) to support SPDC, converting pump photons at 775 nm to signal and idler photons at 1550 nm, with collinear emission at ∼ 60°C. The phasematching condition at degeneracy is very broad even for our 30 mm long crystals, leading to a large spectral bandwidth of the entangled photon pairs of approximately 70 nm, as measured using an optical spectrum analyser. However, the tight energy uncertainty of the narrowband pump photons at 775 nm restricts the photons of any pair to be symmetrically located in frequency around the central wavelength of 1550 nm. Each crystal contains an inscribed waveguide (proton exchange method) with a 9.7 × 7.2 μm2 mode field cross-section at 1550 nm (HC Photonics), guiding only vertical polarised light. Each waveguide is fibre-coupled to a 5.4 μm mode field diameter (MFD) fibre at the input (single mode for the pump), and a polarisation maintaining (PM) 1550 nm fibre with a MFD of 10.4 μm at the output (single mode for the generated photon pairs). Both crystals are pumped by a grating-stabilised narrowband continuous wave (cw) diode laser from Toptica Photonics (DL 100). The laser has a narrow linewidth of ∼ 1 MHz, and can be tuned between 770 nm and 780 nm. A fibre port at the laser head couples around 10 mW of the laser light into a single mode fibre.

Fig. 2 Experimental setup with a cw-laser pumping two ppLN crystals in a Mach-Zehnder interferometer to create polarisation-entangled photon pairs. The pairs are split using a DWDM multiplexer, analysed using polarisation optics and detected with InGaAs single photon detectors. The active phase stabilisation of the interferometric part is achieved with the help of a fibre stretcher.

As shown in Fig. 2, the pump field is split, at a ratio of 50/50, into the two spatial modes of the interferometer with a fibre-based beam splitter (BS) and is then directed to the single mode input fibres of the crystals. Since the quasi phase matching is dependent on the pump polarisation, fibre polarisation controllers (FPC) in each arm are used to adjust the polarisation of the incident pump field to generate pairs with vertical polarisation. The horizontal polarisation component of the pump does not contribute to the SPDC process and is also not guided by the waveguide. The PM fibres at the output face of each crystal are aligned with their slow axis parallel to the polarisation direction of the generated signal/idler pair. Once inside the PM fibre, the polarisation of the pair will remain parallel to the slow axis of the fibre. The two PM fibres are then combined using a fibre-based polarising beam splitter (PBS). This device fuses two input PM fibres into a standard single mode fibre, whereby one of the two PM fibres is turned by 90°. Hence, the polarisation of the pairs from ppLN 2 is turned by 90° with respect to the polarisation of the pair from ppLN 1. Since both crystals initially produced pairs with vertical polarisation |VV〉, the entangled state |ϕ〉 = |HH〉 + e|VV〉 is created, where θ is the phase accumulated in the interferometer, as discussed in Section 2.2. In our setup, the pump and down-converted photons are exclusively transmitted in guided modes (e.g. single-mode fibres and waveguides), making realignments obsolete.

To tune the wavelengths of signal and idler photons, the crystal temperature was controlled by electrical heaters. Degeneracy, where signal and idler photons have the same spectral properties, was achieved by setting the temperature of ppLN1 and ppLN2 to 66.9 °C and 57.5 °C respectively, indicating small differences during production.

2.2. Active phase-stabilisation

The state of the polarisation entanglement is dependent on the phase difference θ of both arms of the Mach-Zehnder interferometer. Since this phase is very sensitive to changes arising from temperature variations and mechanical vibrations, an active stabilisation of the phase inside the interferometer was implemented. A standard telecom add-drop filter (ADF) with a 13 nm wide passband at 1550 nm is used after the interferometric stage to split the laser light (775 nm) from the down-converted light (∼ 1550 nm). The pump light is directed to a phase analyser, consisting of a linear polariser (LP) and a photo-diode. Since the pump light passes the whole Mach-Zehnder interferometer, the change in the phase difference between both arms is transformed to intensity fluctuations after the polariser (set to 45° in the laboratory frame). Phase changes of around π per second were found, clearly indicating the need of an active stabilisation routine. The output signal of the photodiode was fed into a computer, which in turn produced voltages to drive a fibre stretcher in one arm of the interferometer. Stretching the fibre leads to a slight path length difference and hence a change in the relative phase of the interferometer. Although the interferometer is stabelised at 775 nm, the phase for 1550 nm will also be stable. By adding an additional offset with the fibre stretcher, the phase θ can be chosen on demand. For the rest of this work the phase was fixed to θ = 0 to obtain the desired Bell-state: |Φ+=12(|HH+|VV).

2.3. Multi-user distribution

Table 1. Summary of results for the four entangled channel pairs, designated by their ITU numbers and central wavelengths. Coincidence rates and calculated fidelities and purities of the measured states are displayed. Fidelity and purity were calculated both for raw data and after background subtraction.

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2.4. Polarisation analysis and detection

To quantify the degree of polarisation entanglement, a full state tomography was performed for each channel pair. For this measurement, the photons in each channel passed, in free space, a quarter wave plate (QWP) followed by a linear polariser (LP) and long-pass filters (LPF), before being coupled to single mode fibres again. The long-pass filters were used to remove any residual pump light at 775 nm. Fibre-based polarisation controllers (FPC) were introduced before the free space unit to compensate for the unitary rotation of the polarisation state induced by the birefringence of the optical fibre.

3. Results

In contrast to typical SPDC setups where the pump laser is focused onto a small region of the non-liner crystal, the use of a waveguide with strong confinement over a long region of the crystal increases the interaction strength by several orders of magnitude. In the following section we give details of the generation process and detection rates, and characterise entanglement distribution using narrow and broad-band telecom multiplexers.

3.1. Coincidence rates and conversion efficiency

In order to accurately quantify the rates expected from the source, the total optical loss in the system was characterised using a tunable laser diode operated around 1550 nm. The coupling efficiency (ηc) of the waveguide to the fibres (input and output) was estimated to be 50 ± 5%, a figure provided by the manufacturer. The combined transmission of the fibre stretcher and fibre PBS was measured to be 90%. For channel 31, the ADF and DWDM-Demux had a combined transmission of 60%. Lower channel numbers showed higher transmission, whereas higher channel numbers had lower transmission. We believe this is due to the inherent geometry of the DWDM-Demux. Finally, the polarisation analysis units (QWP, LP and LPF) had a transmission of 75%. The total transmission through all optical parts from the waveguides to the inputs of the detectors was therefore ηopt = 20%.

To characterize the coincidence rates between signal and idler photons, a single crystal (ppLN 2) was used, and the pump power (Ppump) was set to 18 μW. The detected single rate (signal photons) in channel 37 was 2600 counts per seconds (thereafter, c/s) using DET1 at 1% duty cycle (fgate = 100 kHz). At this setting, the detector had a dark count rate of approx. 130 c/s. As expected from conservation of energy, idler photons were found in channel 31 and a coincidence rate (Rc) of 75 c/s was detected at DET2. The coincidence to single ratio was found to be 2.9%, which compares favourably with the expected ratio of 3%, given by the product of ηopt and ηDET2. In order to improve Rc, we increased the gate frequency of DET1 to 1MHz. This increased the single rate to 38000 c/s (of which 9000 c/s were dark counts) and Rc to 450 c/s, yielding a ratio of 1.5% only. We believe that the single rate and dark count rate is highly increased by afterpulsing effects. This can also be seen by the nearly 12-fold increase in the single rate, although only a 6-fold increase would be anticipated from the actual gate rate on DET1, which was down to fgate = 620 kHz due to saturation. However the coincidence rate did increase by a factor of 6, which furthermore supports our hypothesis of afterpulsing. Waveguide ppLN 1 showed a similar behaviour, but with a lower single and coincidence rate. We attribute this to lossier fibre-waveguide couplings. To achieve equal coincidence rates between the two crystals, as required for Bell-state production, the effective pump power into ppLN 2 was reduced by slightly turning the input polarisation away from optimum. We also tested the quality of our fibre-pigtailed crystals by second-harmonic-generation (SHG). This reverse process to SPDC converts two pump photons at a wavelength around 1550 nm to a signal photon at 775 nm. We measured overall SHG-efficiencies of 186%/W and 218%/W for the crystals ppLN1 and ppLN2 respectively, again observing a slight difference in the conversion efficiency.

The fibre coupled brightness (B) of the source can be calculated by taking into account the detector efficiencies and bandwidth (Δν) of the photons. Using the data from the 1% duty cycle run, this results in B = Rc/(ηDET1ηDET2ηduty)/Ppumpν = 4.5×105 pairs/s/mW/GHz, which is several orders of magnitude higher than in comparable sources using nonlinear crystals without waveguides [28

28. M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express 17, 23153–23159 (2009). [CrossRef]

, 29

29. F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express 20, 9640–9649 (2012). [CrossRef] [PubMed]

].

Since the crystals are fibre-coupled with known losses, an attempt was made to estimate the intrinsic conversion efficiency, i.e. the probability to create a photon pair given a single pump photon. This measurement was performed with an input power of 0.62 mW of 775 nm light, which yielded a SPDC output power of 1.7 nW at 1550 nm as measured with a standard power meter. The measured conversion efficiency is hence 2.74 × 10−6. Including the losses of the fibre coupling, ηc, the intrinsic efficiency of the SPDC inside the waveguide is even larger and estimated to be 1.1 ± 0.1 × 10−5. Hence, for every ∼ 105 pump photons, one signal-idler pair is generated. This is in excellent agreement with a theoretical calculation of the conversion efficiency [30

30. M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479–7488 (2007). [CrossRef] [PubMed]

] which yields 1.1 × 10−5 for the ppLN waveguide used in our measurements.

3.2. Tomographic measurements on entangled channels

The polarisation state of each entangled channel pair was analysed using a state tomography measurement [31

31. D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]

]. Coincidences were measured in 16 polarisation settings (HH, HV, HP, HR, VH, VV, VP, VR, PH, PV, PP, PR, RH, RV, RP and RR), where H,V,P and R stand for horizontal, vertical, +45° and right circular polarisation respectively. All coincidences, averaged over 20 seconds, were recorded with an input power of 18 μW for each crystal and a duty cycle of 10% for DET1. The maximal coincidence rates measured were found to be around 450 c/s, as shown in Table 1. As previously mentioned, each channel of the DWDM-Demux has different insertion losses affecting the coincidence rates between channel pairs. Density matrices (ρ), calculated from the raw coincidence rates for each channel pair, can be seen in Fig. 3. Fidelities (〈Φ+|ρ+〉) and purities (Tr(ρ2)) for all four entangled channel pairs were also obtained, and are listed in Table 1. The fidelities have values around 93% indicating a high degree of entanglement of the raw data. This raw fidelity value yields a quantum bit error of ∼ 3%, low enough to establish a secret key between parties using the BBM92 QKD protocol [32

32. C. Bennett, G. Brassard, and N. Mermin, “Quantum Cryptography without Bell theorem,” Phys. Rev. Lett. 68, 557–559 (1992). [CrossRef] [PubMed]

]. The observed fidelity is also in very good agreement with a study predicting an entanglement visibility of 93% for entanglement distribution using a DWDM-Demux [33

33. J. Ghalbouni, I. Agha, R. Frey, E. Diamanti, and I. Zaquine, “Experimental wavelength-division-multiplexed photon-pair distribution,” Optics Lett. 38, 34–36 (2013). [CrossRef]

]. With subtraction of the background of ∼ 15 c/s, as measured by shifting the coincidence window, fidelity and purity values of up to 99% are observed, also listed in Table 1. The accidental coincidences consist primarily of higher order emissions and afterpulsing, while coincidences due to dark counts only contributed 0.5 c/s. The above values show that the source is producing entangled states at very high fidelity over all eight channels. Even when considering only one pair of DWDM-Demux channels, our source has the highest reported coincidence rate for a raw fidelity above 90% in similar χ2 waveguide sources [21

21. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarisation-entangled photon pairs at 1500 nm using two PPLN waveguides,” Electronics Lett. 39, 621–622 (2003). [CrossRef]

, 34

34. A. Yoshizawa and H. Tsuchida, “Violation of Bell’s inequality in 1550 nm band without subtraction of accidental coincidences,” Japanese Journal of applied Physics 44, L375–L377 (2005). [CrossRef]

37

37. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ(2)processes in a periodically poled LiNbO3ridge waveguide,” Opt. Express 19, 16032–16043 (2011). [CrossRef] [PubMed]

].

Fig. 3 Real part of the density matrices obtained from tomography measurements (raw coincidences) for each entangled channel pair. The elements of the imaginary parts are all smaller than 0.07.

3.3. Visibility measurements on entangled channels in a CWDM-grid

The spectrum of our source extends over 5 channels of the widely deployed CWDM telecom wavelength grid. Less stringent requirements on the wavelength accuracy leads to cheaper components and high availability paves the way for easy integration of QKD-systems in existing telecom networks. Therefore we replaced the ADF and DWDM-Demux with a 5 channel CWDM-Demux, and sliced the SPDC spectrum into 20 nm wide channels, with a 13 nm passband in each channel. The center channel at 1551 nm was used for the phase stabilisation. In order not to saturate our detectors we reduced the pump power to 1 μW per crystal and recorded a coincidence rate of around 200 c/s which is in agreement with the increased bandwidth of the channels. However visibility measurements for the entangled pairs in the channels with the central wavelength of 1531–1571 nm (1) and 1511–1591 nm (2) showed only values of V1 = 86.8% and V2 = 87.5%, respectively. With background subtraction the values increased somewhat to V1 = 91.1% and V2 = 90.9%, but were still below the near 100% mark achieved with the DWDM-Demux. We believe that the reduction of visibility is caused by the wavelength-dependent birefringence in the fibre. The large bandwidth of the CWDM-Demux causes different wavelenghts to experience different polarisation rotations in the optical fibre. Since our polarisation controller can only correct for a single specific rotation, a large part of the spectrum will deviate from the input polarisation state and hence cause a decrease in visibility. For this reason and because of the effects of chromatic dispersion, discussed above, it is important to optimise the source for a high spectral brightness (B) in order to limit the bandwidth of each channel as much as possible.

4. Multi-user entanglement distribution — “Any Alice to any Bob” network application

Fig. 4 Software-defined network (SDN) realisation with two optical switches for active, on-demand distribution of entanglement. Depending on the choice of the switch setting (I, II or III), different user pairs will share entangled photons for quantum information applications.

We implemented such a SDN for 4 users, by incorporating two opto-mechanical switches from Cube Optics into four of the fibres leaving the DWDM-Demux. Both switches feature a 2 × 2 port design (two inputs and two outputs) and are concatenated to allow for a switching of the entangled inputs to any output configuration. The switches had typical insertion losses of around 8% expect one input which showed a higher loss of 15%. The distribution of bipartite entanglement between any two users out of four, was achieved by using three possible switch configurations, as schematically depicted in Fig. 4 (b).

Coincidence rates and polarization correlations for all possible switch settings were measured again. The rates together with the calculated state visibilities and purities for all user pairs are shown in Table 2. Depending on the additional losses caused by the switches the coincidence rates are only slightly decreased, the visibilities and purities show again a very high degree of entanglement between any pair of users.

Table 2. Summary of results for the three switch settings in the SDN. Each setting results in two 2-party sharing of entangled states. Coincidence rates, calculated fidelities and purities (with and without background counts) for each user pair are listed.

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The switch box can be expanded to a NxM architecture with N wavelength channels serving M users by using well-established mathematical methods developed for telecom industry using a combination of 2×2-switches as the basic element. For standard telecommunication architectures, the requirement of non-blocking behaviour is usually important in order to guarantee any possible connectivity from one of the N inputs to any of the M output ports independent of other connections through the switching network. For the purpose of distribution of entangled photon pairs this very restrictive requirement is not necessary, because two users requesting entangled photon pairs to establish quantum correlation, for e.g. a secure QKD-link, are in generally not interested in: (a) which pair of wavelength (i.e. ITU-channels as indicated in Table 1) of the possible N/2 they will receive and (b) which photon of a pair. We therefore believe that entanglement distribution networks scale better in terms of loss than traditional telecommunication networks. In our example shown in Fig. 4 (b), we distribute N=4 different wavelengths of photons to M=4 users using only two 2×2 switches. A traditional non-blocking Clos-network would require 6 switches (three concatenated switches in parallel), and each photon would therefore experience three times the loss of a single switch. Moreover, each doubling of the number of input pairs would require the addition of two rows of switches, increasing the overall loss. A constant loss, independent of the number of users, could be achieved using a mirror array, typically based on Micro-Electro-Mechanical-System (MEMS) technology, which is commercially available for up to N=M=192 channels.

5. Conclusion

The observed entanglement fidelities after distribution were very high (93%), and reached up to 99% with background substraction. Although we report the highest coincidence rates for a fibre pigtailed waveguide source, the rate was still limited by InGaAs APDs which were used in a gated mode with a maximal duty cycle of 10%. However advanced detector technology for the near-infrared is now commercially available and will remedy this problem in future.

Acknowledgments

We would like to thank Michael Hentschel and Sven Ramelow for technical assistance. This work was supported by the Austrian Science Foundation FWF ( TRP-L135 and SFB-1520), the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, Canadian Institute for Advanced Research, Ontario Research Fund, and Industry Canada. We would also like to thank the Institute for Quantum Optics and Quantum Information, Vienna, for financial assistance in obtaining the waveguides. I.H. thanks the Institute for Quantum Computing, Waterloo, Canada, for hosting her during the writing-up phase of this article.

References and links

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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]

3.

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007). [CrossRef] [PubMed]

4.

T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. H. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over optical fiber,” Opt. Express 16, 19118–19126 (2008). [CrossRef]

5.

A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Loruenser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys. 11, 085002 (2009). [CrossRef]

6.

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11, 085002 (2009). [CrossRef]

7.

M. P. Peloso, I. Gerhardt, C. Ho, A. Lamas-Linares, and C. Kurtsiefer, “Daylight operation of a free space, entanglement-based quantum key distribution system,” New J. Phys. 11, 045007 (2009). [CrossRef]

8.

M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fuerst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Laenger, M. Legre, R. Lieger, J. Lodewyck, T. Loruenser, N. Luetkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009). [CrossRef]

9.

M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legre, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Laenger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19, 10387–10409 (2011). [CrossRef] [PubMed]

10.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999). [CrossRef]

11.

H. Buhrman, R. Cleve, and W. Van Dam, “Quantum entanglement and communication complexity,” Siam Journal on Computing 30, 1829–1841 (2001). [CrossRef]

12.

ITU-T recommendation G.694.2 (2003).

13.

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, 4337–4341 (1995). [CrossRef] [PubMed]

14.

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electronics Lett. 37, 26–28 (2001). [CrossRef]

15.

K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Express 31, 1905–1907 (2006).

16.

S. X. Wang and G. S. Kanter, “Robust multiwavelength all-fiber source of polarization-entangled photons with built-in analyzer alignment signal,” IEEE Journal of selected topics in quantum electronics 15, 1733–1740 (2009). [CrossRef]

17.

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007). [CrossRef]

18.

E. Meyer-Scott, V. Roy, J.-P. Bourgoin, B. L. Higgins, L. K. Shalm, and T. Jennewein, “Generating polarization-entangled photon pairs using cross-spliced birefringent fibers,” Opt. Express 21, 6205–6212 (2012). [CrossRef]

19.

E. Y. Zhu, Z. Tang, L. Qian, L. G. Helt, M. Liscidini, J. E. Sipe, C. Corbari, A. Canagasabey, M. Ibsen, and P. G. Kazansky, “Direct generation of polarization-entangled photon pairs in a poled fiber,” Phys. Rev. Lett. 108(2012). [CrossRef]

20.

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, 16052–16057 (2008). [CrossRef] [PubMed]

21.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarisation-entangled photon pairs at 1500 nm using two PPLN waveguides,” Electronics Lett. 39, 621–622 (2003). [CrossRef]

22.

H. Huebel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Loruenser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express 15, 7853–7862 (2007). [CrossRef]

23.

B. Qi, W. Zhu, L. Qian, and H.-K. Lo, “Feasibility of quantum key distribution through a dense wavelength division multiplexing network,” New J. Phys. 12, 103042 (2010). [CrossRef]

24.

R. E. Warburton, M. Itzler, and G. S. Buller, “Free-running, room temperature operation of an InGaAs/InP single-photon avalanche diode,” Appl. Phys. Lett. 94, 071116 (2009). [CrossRef]

25.

Z. Yan, D. R. Hamel, A. K. Heinrichs, X. Jiang, M. A. Itzler, and T. Jennewein, “An ultra-low noise telecom wavelength free running single photon detector using negative feedback avalanche diode,” Rev. Sci. Instrum. 83, 073105 (2012). [CrossRef]

26.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008). [CrossRef] [PubMed]

27.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nature Photonics 7, 210–214 (2013). [CrossRef]

28.

M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express 17, 23153–23159 (2009). [CrossRef]

29.

F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express 20, 9640–9649 (2012). [CrossRef] [PubMed]

30.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479–7488 (2007). [CrossRef] [PubMed]

31.

D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]

32.

C. Bennett, G. Brassard, and N. Mermin, “Quantum Cryptography without Bell theorem,” Phys. Rev. Lett. 68, 557–559 (1992). [CrossRef] [PubMed]

33.

J. Ghalbouni, I. Agha, R. Frey, E. Diamanti, and I. Zaquine, “Experimental wavelength-division-multiplexed photon-pair distribution,” Optics Lett. 38, 34–36 (2013). [CrossRef]

34.

A. Yoshizawa and H. Tsuchida, “Violation of Bell’s inequality in 1550 nm band without subtraction of accidental coincidences,” Japanese Journal of applied Physics 44, L375–L377 (2005). [CrossRef]

35.

Y.-K. Jiang and A. Tomita, “Highly efficient polarization-entangled photon source using periodically poled lithium niobate waveguides,” Opt. Commun. 267, 278–281 (2006). [CrossRef]

36.

H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express 16, 12460–12468 (2008). [CrossRef] [PubMed]

37.

S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ(2)processes in a periodically poled LiNbO3ridge waveguide,” Opt. Express 19, 16032–16043 (2011). [CrossRef] [PubMed]

38.

Z.-Y. Zhou, Y.-K. Jiang, D.-S. Ding, B.-S. Shi, and G.-C. Guo, “Actively switchable nondegenerate polarization-entangled photon-pair distribution in dense wave-division multiplexing,” Phys. Rev. A 87, 045806 (2013). [CrossRef]

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(060.4265) Fiber optics and optical communications : Networks, wavelength routing
(060.5565) Fiber optics and optical communications : Quantum communications
(270.5568) Quantum optics : Quantum cryptography

ToC Category:
Quantum Optics

History
Original Manuscript: August 15, 2013
Revised Manuscript: September 20, 2013
Manuscript Accepted: September 21, 2013
Published: November 15, 2013

Citation
I. Herbauts, B. Blauensteiner, A. Poppe, T. Jennewein, and H. Hübel, "Demonstration of active routing of entanglement in a multi-user network," Opt. Express 21, 29013-29024 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-29013


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References

  1. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys.84, 777–838 (2012). [CrossRef]
  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74, 145–195 (2002). [CrossRef]
  3. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett.98, 230501 (2007). [CrossRef] [PubMed]
  4. T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. H. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over optical fiber,” Opt. Express16, 19118–19126 (2008). [CrossRef]
  5. A. Treiber, A. Poppe, M. Hentschel, D. Ferrini, T. Loruenser, E. Querasser, T. Matyus, H. Hübel, and A. Zeilinger, “A fully automated entanglement-based quantum cryptography system for telecom fiber networks,” New J. Phys.11, 085002 (2009). [CrossRef]
  6. T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys.11, 085002 (2009). [CrossRef]
  7. M. P. Peloso, I. Gerhardt, C. Ho, A. Lamas-Linares, and C. Kurtsiefer, “Daylight operation of a free space, entanglement-based quantum key distribution system,” New J. Phys.11, 045007 (2009). [CrossRef]
  8. M. Peev, C. Pacher, R. Alleaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fuerst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Laenger, M. Legre, R. Lieger, J. Lodewyck, T. Loruenser, N. Luetkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys.11, 075001 (2009). [CrossRef]
  9. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legre, S. Robyr, P. Trinkler, L. Monat, J. B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Laenger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express19, 10387–10409 (2011). [CrossRef] [PubMed]
  10. M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A59, 1829–1834 (1999). [CrossRef]
  11. H. Buhrman, R. Cleve, and W. Van Dam, “Quantum entanglement and communication complexity,” Siam Journal on Computing30, 1829–1841 (2001). [CrossRef]
  12. ITU-T recommendation G.694.2 (2003).
  13. 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, 4337–4341 (1995). [CrossRef] [PubMed]
  14. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electronics Lett.37, 26–28 (2001). [CrossRef]
  15. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Express31, 1905–1907 (2006).
  16. S. X. Wang and G. S. Kanter, “Robust multiwavelength all-fiber source of polarization-entangled photons with built-in analyzer alignment signal,” IEEE Journal of selected topics in quantum electronics15, 1733–1740 (2009). [CrossRef]
  17. Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A75, 023803 (2007). [CrossRef]
  18. E. Meyer-Scott, V. Roy, J.-P. Bourgoin, B. L. Higgins, L. K. Shalm, and T. Jennewein, “Generating polarization-entangled photon pairs using cross-spliced birefringent fibers,” Opt. Express21, 6205–6212 (2012). [CrossRef]
  19. E. Y. Zhu, Z. Tang, L. Qian, L. G. Helt, M. Liscidini, J. E. Sipe, C. Corbari, A. Canagasabey, M. Ibsen, and P. G. Kazansky, “Direct generation of polarization-entangled photon pairs in a poled fiber,” Phys. Rev. Lett.108(2012). [CrossRef]
  20. 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. Express16, 16052–16057 (2008). [CrossRef] [PubMed]
  21. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Generation of polarisation-entangled photon pairs at 1500 nm using two PPLN waveguides,” Electronics Lett.39, 621–622 (2003). [CrossRef]
  22. H. Huebel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Loruenser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express15, 7853–7862 (2007). [CrossRef]
  23. B. Qi, W. Zhu, L. Qian, and H.-K. Lo, “Feasibility of quantum key distribution through a dense wavelength division multiplexing network,” New J. Phys.12, 103042 (2010). [CrossRef]
  24. R. E. Warburton, M. Itzler, and G. S. Buller, “Free-running, room temperature operation of an InGaAs/InP single-photon avalanche diode,” Appl. Phys. Lett.94, 071116 (2009). [CrossRef]
  25. Z. Yan, D. R. Hamel, A. K. Heinrichs, X. Jiang, M. A. Itzler, and T. Jennewein, “An ultra-low noise telecom wavelength free running single photon detector using negative feedback avalanche diode,” Rev. Sci. Instrum.83, 073105 (2012). [CrossRef]
  26. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008). [CrossRef] [PubMed]
  27. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nature Photonics7, 210–214 (2013). [CrossRef]
  28. M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express17, 23153–23159 (2009). [CrossRef]
  29. F. Steinlechner, P. Trojek, M. Jofre, H. Weier, D. Perez, T. Jennewein, R. Ursin, J. Rarity, M. W. Mitchell, J. P. Torres, H. Weinfurter, and V. Pruneri, “A high-brightness source of polarization-entangled photons optimized for applications in free space,” Opt. Express20, 9640–9649 (2012). [CrossRef] [PubMed]
  30. M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express15, 7479–7488 (2007). [CrossRef] [PubMed]
  31. D. James, P. Kwiat, W. Munro, and A. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001). [CrossRef]
  32. C. Bennett, G. Brassard, and N. Mermin, “Quantum Cryptography without Bell theorem,” Phys. Rev. Lett.68, 557–559 (1992). [CrossRef] [PubMed]
  33. J. Ghalbouni, I. Agha, R. Frey, E. Diamanti, and I. Zaquine, “Experimental wavelength-division-multiplexed photon-pair distribution,” Optics Lett.38, 34–36 (2013). [CrossRef]
  34. A. Yoshizawa and H. Tsuchida, “Violation of Bell’s inequality in 1550 nm band without subtraction of accidental coincidences,” Japanese Journal of applied Physics44, L375–L377 (2005). [CrossRef]
  35. Y.-K. Jiang and A. Tomita, “Highly efficient polarization-entangled photon source using periodically poled lithium niobate waveguides,” Opt. Commun.267, 278–281 (2006). [CrossRef]
  36. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express16, 12460–12468 (2008). [CrossRef] [PubMed]
  37. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ(2)processes in a periodically poled LiNbO3ridge waveguide,” Opt. Express19, 16032–16043 (2011). [CrossRef] [PubMed]
  38. Z.-Y. Zhou, Y.-K. Jiang, D.-S. Ding, B.-S. Shi, and G.-C. Guo, “Actively switchable nondegenerate polarization-entangled photon-pair distribution in dense wave-division multiplexing,” Phys. Rev. A87, 045806 (2013). [CrossRef]

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