OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 25 — Dec. 12, 2005
  • pp: 9961–9969
« Show journal navigation

Quantum key distribution over an installed multimode optical fiber local

Naoto Namekata, Shigehiko Mori, and Shuichiro Inoue  »View Author Affiliations


Optics Express, Vol. 13, Issue 25, pp. 9961-9969 (2005)
http://dx.doi.org/10.1364/OPEX.13.009961


View Full Text Article

Acrobat PDF (178 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We have investigated the possibility of a multimode fiber link for a quantum channel. Transmission of light in an extremely underfilled mode distribution promises a single-mode–like behavior in the multimode fiber. To demonstrate the performance of the fiber link we performed quantum key distribution, on the basis of the BB84 four-state protocol, over 550 m of an installed multimode optical fiber local area network, and the quantum-bit-error rate of 1.09 % was achieved.

© 2005 Optical Society of America

1. Introduction

Quantum communication is one of the most rapidly growing and exciting fields of physics in recent years. Its most mature application is quantum key distribution (QKD), which was invented by Bennett and Brassard in 1984 and which ensures the distribution of a secret key between two parties [1

1 . C. H. Bennett and G. Brassard , “ Quantum cryptography: Public key distribution and coin tossing ,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing ( Institute of Electrical and Electronics Engineers, New York , 1984 ), pp. 175 – 179 .

]. Following the first experimental demonstration of QKD over a distance of 40 cm in free space [2

2 . C. H. Bennett , F. Bessette , G. Brassard , L. Salvail , and J. Smolin , “ Experimental quantum cryptography ,” J. Crtptol. 5 , 3 – 28 ( 1992 ).

], development of a long-distance fiber-optic QKD system has been the main issue in the way of putting QKD into practice.

In this paper, we show that the long-distance QKD system designed for operation over standard single-mode fibers can also be used to distribute keys over multimode fibers. QKD over a multimode fiber is very important in practice, because we can use any installed LANs for a quantum channel without any additional costs. First, we consider a possibility of a graded-index (GI) multimode fiber for a quantum channel, and we show that transmission of light in an underfilled mode distribution is available for a quantum channel. Then, we show experimental results of a QKD using an installed GI multimode fiber link. The time-multiplexed interferometer that we adopted as a QKD system is similar to that presented in Ref. [5

5 . D. Bethune and W. Risk , “ An autocompensation fiber-optic quantum cryptography system based on polarization splitting of light ,” IEEE J. Quantum Electron. 36 , 340 – 347 ( 2000 ). [CrossRef]

], except that the losses at the receiver’s station are minimized by use of polarization-maintaining optical fibers and LiNbO3 waveguide optical modulators [13

13 . N. Namekata and S. Inoue , “ Fiber-optic quantum key distribution at 1550 nm ” in Proceedings of the ERATO Workshop on Quantum Information Science (JST, Tokyo, 2002 ), pp. 96 – 97 .

]. The losses at the receiver’s station must be as low as possible in QKD over a multimode fiber, because the coupling losses between the single-mode fiber at the receiver’s station and the multimode fiber are fairly large.

2. Measurement of group velocity dispersion

Fig. 1. Illustration of the mode distribution in a graded index multimode fiber: (a)Equivalent mode distribution (b) Underfilled mode distribution

The single-mode fiber enables light to propagate in a single mode with a small field diameter. Therefore, when a butt junction is used through which light from the single-mode fiber is coupled into a multimode fiber, only one mode can be excited in the center of the core of the multimode fiber. The remarkable point is whether the input state in the extremely underfilled mode distribution is destroyed or not in the multimode fiber. In order to demonstrate it, we measured GVDs in a multimode fiber. Figure 2 shows the experimental setup for GVD measurements based on photon counting [14

14 . N. Brunner , V. Scarani , M. Wegmuller , M. Legre , and N. Gisin , “ Direct measurement of superluminal group velocity and signal velocity in an optical fiber ,” Phys. Rev. Lett. 93 , 203902 ( 2004 ). [CrossRef] [PubMed]

]. A 1550 nm distributed feedback (DFB) diode laser (Hama-matsu PLP-01) sends ≃ 50 ps pulses to Fiber 1. They are coupled into Fiber 2 through the butt junction and finally detected by a single-photon detector with a 1 m single-mode fiber pigtail. Here, the standard FC/PC couplers (fiber-to-fiber coupler) were used to connect these fibers. The detector is InGaAs/InP avalanche photodiode (EPM239BA Epitaxx) operated by a gated mode [9

9 . N. Namekata , Y. Makino , and S. Inoue , “ Single-photon detector for long-distance fiber optic quantum key distribution ,” Opt. Lett. 27 , 954 – 956 ( 2002 ). [CrossRef]

]. Here, the gate width is set to 20 ns, which is much longer than the light pulse width. (More details of the single-photon detector are in Section 3.) The multichannel scaler (MCS) records an arrival time of photons in the pulse. We can obtain a profile of light pulses from the tested fiber by constructing a histogram of the time of each photon’s arrival. We tested three combinations of fibers (see Table 1). The GI multimode fiber we used has NA of 0.275 and core/cladding of 62.5/125 (the size is in microns), and the single-mode fiber has NA of 0.11 and core/cladding of 9/125. In Test 1, we measured the pulse width after the ideal single-mode transmission in the 50 m single-mode fiber. In Tests 2 and 3, we measured the pulse width after transmission in the 550 m GI multimode fiber (an installed LAN). Here, notice that the input states of Tests 2 and 3 are the EMD for the GI multimode fiber and the single-mode (the extremely underfilledmode distribution), respectively. Measured pulse profiles of these tests are shown in Fig. 3. Although the laser pulse width is ~50 ps, measured pulse width is ~300 ps (Test 1). The 50 m long (dispersion shifted) single-mode fiber has the dispersion slope of only ~ 1ps/nm/km 2 (at the zero dispersion wavelength of 1550 nm). Therefore, the pulse width was not widened via the dispersion of the single-mode fiber, and it is caused by the timing resolution of the single-photon detector [8

8 . D. Stucki , G. Ribordy , A. Stefanov , H. Zbinden , J. G. Rarity , and T. Wall , “ Photon counting for quantum key distribution with Peltier coold InGaAs/InP APD’s ,” J. Modern Opt. 48 , 1967 – 1982 ( 2001 ). [CrossRef]

]. However, the timing resolution of the measurement system is enough to confirm that the pulse width is widened via the large GVD in the GI multimode fiber (Test 2). The remarkable result is in Test 3. Although the light pulse passes through the GI multimode fiber, the GVD is very small, and the profile of the light pulse is almost identical with that of Test 1. This result suggests that almost all the energy of the light pulse is in the single mode and a small fraction of the energy is shifted to higher-order propagation modes, although the light pulse propagates in the GI multimode fiber.

Fig. 2. Measurement of group velocity dispersion based on a photon counting.
Fig. 3. Profiles of light pulses after transmission through (a) only the single-mode fiber (Test 1), (b) only the multimode fiber (Test 2), (c) the multimode fiber after the single-mode fiber (Test 3).

Table 1. Tested combination of fibers

table-icon
View This Table
| View All Tables

To obtain another aspect of the property, we also measured the NA of an output from the GI multimode fiber through a conventional knife-edge experiment. When the combination of fibers matched that of Test 2, the measured NA was 0.27. The result is in good agreement with the NA of GI multimode fiber. On the other hand, when the combination of fibers matched that of Test 3, the measured NA was 0.12. This value is close to the NA of the single-mode fiber rather than the multimode fiber. The butt junction through which light from the GI multimode fiber is coupled into the single-mode fiber usually has large optical losses (~30 dB), resulting from a mismatch of the core diameter and the NA. However, since the NA and the mode field diameter in the extremely underfilled distribution match the single-mode fiber, optical losses of the junction were reduced to 3~5 dB. Moreover, the energy rejected at the junction is in higher-order modes excited in the multimode fiber. In other words, through the filtering effect, only the energy having the single-mode behavior in the GI multimode fiber is efficiently coupled into the single-mode fiber. As described above, the extremely underfilled transmission improves performances of the GI multimode fiber link.

However, when the light propagates through the much longer GI multimode fiber, the more energy propagating in GI multimode fiber is in higher-order modes. This indicates that the underfilled behavior deteriorates and the propagation-mode distribution would eventually reach the EMD. In the EMD, the optical losses in the connection between the GI multimode fiber and the single-mode fiber will be huge. Therefore, a necessary length for the transition to the EMD will set a limit of the communication distance in the GI multimode fiber channel. Assuming that the fiber is a high-quality silica fiber, the necessary length is generally more than 10 km. However, the length may be shortened by an environment of a fiber channel, for example, a stress on the fiber advances the transition to the EMD.

3. Experimental setup

Each orthogonally polarized pulse pair arrives at Alice’s station in unspecified elliptical polarization states. They pass through a 50/50 fiber-optic coupler, an attenuator, and Alice’s phase modulator PMA (PM4-140-15). The Faraday mirror reflects the pulses and rotates the polarization states by 90 degrees, which interchanges the elliptical polarization states of P1 and P2. Due to this polarization interchange, P1 and P2 will accumulate equal overall phase shifts in the course of completing a round trip back to PBS2, provided that the properties of the optical path change slowly relative to the time required for a round trip. If Alice deliberately violates this condition by rapidly stepping the voltage VA applied to PMA between the times that P1 and P2 pass through it, she can encode information as a differential phase shift ϕA = ϕ P2 - ϕ P1 between the P1 and P2 pulses. She implements Bennett’s four-state protocol for encoding key data by randomly choosing between voltages VA = -1.45, 0, 1.45, and 2.9 V that give the four phase shifts ϕA = -π/2,0, π/2, and π.

Fig. 4. Schematic diagram of quantum key distribution system: C Circulator; PBS1, PBS2 Polarizing beam splitters; SMF Single-mode fiber; PMF Polarization-maintaining fiber; MMF Multimode fiber; FC 50/50 fiber-optic coupler; AT Attenuator; PMA, PMB Phase modulators; FM Faraday mirror; D1, D2 Single-photon detectors; PG1, PG2 Pulse generators; AWGA, AWGB; Arbitrary waveform generators.

The returning pulse pair is attenuated to the single-photon level as it leaves Alice’s station. The Faraday orthoconjugation guarantees that the returning pulse components arrive at PBS2 linearly polarized and orthogonal to their outgoing polarization. Thus the P1 component arrives vertically polarized and is sent through the delay loop, while the initially delayed P2 component arrives horizontally polarized and passes straight through PBS2. For each returning pulse pair, Bob can use the phase modulator PMB to give a phase shift ϕB to P1 as it passes through the delay loop. By randomly choosing ϕB = 0 or -π/2, Bob can switch between two nonorthogonal bases for analyzing the returning photons, as required by the four-state protocol.

The P1 and P2 components then arrive simultaneously at PBS2 and recombine into a single pulse P0 with a polarization state that depends only on the difference of the applied phase shift, Δϕ = ϕA - ϕB. The polarization of P0 is oriented along the fast axis of the PMF connected to PBS1 when the phase difference Δϕ = 0. Then the P0 is reflected by PBS1 and detected by the single-photon detector D2. On the other hand, the polarization of P0 is oriented along the slow axis of the PMF when the phase difference Δϕ = π. Then the P0 passes through PBS1 and is detected by the single-photon detector D1. For mismatched basis choices, where Δϕ = -π/2, π/2, or 3π/2, the recombined pulses will be circularly polarized, and PBS1 will randomly divide the photons between the two detectors with equal probability.

Our single-photon detectors are Epitaxx EPM239BA APDs operated in gated mode at -55 degree Celsius [9

9 . N. Namekata , Y. Makino , and S. Inoue , “ Single-photon detector for long-distance fiber optic quantum key distribution ,” Opt. Lett. 27 , 954 – 956 ( 2002 ). [CrossRef]

]. The DFB laser triggers first a delay generator (Stanford Research Systems DG535), which provides the timing of our QKD system. Then the delay generator triggers pulse generators (PG1 and PG2) that generate gate pulses. Each gate pulse has an amplitude of 4.5 V and a full width at a half-maximum of approximately 1 ns. The repetition frequencies of the gate pulses, i.e., laser pulses, are 9 kHz for the 10.5 km spool and 100 kHz for the 550 m LAN, which are limited by the longest delay in the system. The delays are set such that the photons impinge upon the APD’s sensitive area when it is gated on. A gated passive quenching circuit [15

15 . S. Cova , M. Ghioni , A. Lacaita , C. Samori , and F. Zappa , “ Avalanche photodiodes and quenching circuits for single-photon detection ,” Appl. Opt. 35 , 1956 – 1963 ( 1996 ). [CrossRef] [PubMed]

] with a 47 kΩ series resistance providing the dc bias and the APDs are placed in a cryostat. The gate pulse was superimposed on the dc bias voltage and the signal was measured over a 50 Ω resistance. We controlled the excess bias voltage above breakdown by adjusting the dc bias voltage. In the QKD experiments, the excess bias voltage was set to 3.5 V. The avalanche signal was finally discriminated and registered by a photon counter (Stanford Research Systems SR 400). The delay generator also triggers arbitrary waveform generators (AWGA and AWGB), which control the timing when the phase modulators are biased.

Fig. 5. Count rates of single-photon detectors D1 and D2 versus Alice’s modulator voltage. The average photon number per pulse was ≃ 2, and Bob’s phase shift ΔϕB was set to 0 or -π/2. (a) 10.5 km single-mode fiber spool, (b) 550 m multimode fiber local area network.

4. Experimental results

The interference fringes for the 10.5 km spool and the 550 m LAN are shown in Fig. 5. The single-photon counting was performed using D1 and D2 while changing Alice’s modulator voltage from -5 to 5 V when ΔϕB = 0 or -π/2. Here the average photon number per pulse was set to ~2 by the monitoring of another output of the 50/50 coupler using one of the single-photon detectors. The count rate of D1 results from attenuation by the 10.5 km spool (L 1 ~2.4 dB) or the 550 m LAN (L 2 ~5 dB including the coupling losses between the multimode and single-mode fibers), the optical losses leading to D1 in Bob’s station (L D1 ~4.0 dB), and the quantum efficiency of D1 (η 1 ~ 23 %). On the other hand, the count rate of D2 results from attenuation by L 1 or L 2, the optical losses leading to D2 in Bob’s station (L D2 ~3.5 dB), and the quantum efficiency of D2 (η 2 ~19%). Here the optical losses L D1 and L D2 were measured by connecting the 50/50 coupler directly to PBS2. The optical losses in Bob’s station are much smaller than those in Ref. [5

5 . D. Bethune and W. Risk , “ An autocompensation fiber-optic quantum cryptography system based on polarization splitting of light ,” IEEE J. Quantum Electron. 36 , 340 – 347 ( 2000 ). [CrossRef]

] (~ 10dB), which are realized by rotating PMFs instead of inserting polarization rotators and using a low-loss LiNbO3 waveguide optical modulator.

The fringe visibility V1 at the output port leading to D1 is 0.9990, and V2 at the output port leading to D2 is 0.9975 for the 10.5 km single-mode fiber spool. On the other hand, the visibilities V1 and V2 for the 550 m LAN are 0.9973 and 0.9967, respectively. Here the optical losses of the 550 m LAN are approximately 2 dB. Although the optical losses of GI multimode fiber are only 0.3 dB/km, attenuation by several connectors in the LAN results in such large optical losses. In addition, the optical losses from the LAN to Bob’s station are approximately 3 dB, which is caused by NA and core diameter mismatches between the multimode and the single-mode fiber. As described in Section 2, the relatively small optical losses indicate that only a few modes are excited in the 550 m GI multimode fiber LAN. The single-mode fiber in Bob’s station plays the role of a filter to reject higher-order modes excited in the LAN. Therefore only the energy having the single-mode behavior in the LAN was efficiently coupled into the single-mode fiber in Bob’s station. As a result, the high fringe visibilities were obtained, although the LAN was composed of the multimode fiber.

Table 2. Summary of quantum-bit-error rates and bit rates

table-icon
View This Table
| View All Tables

In the case that the fiber channel is the GI multimode fiber, it seems that the channel security is lower than the single-mode fiber channel, resulting from a facility for extracting photons in higher-order modes. However, this eavesdropping is the same as the conventional beam-splitting attack, because photons in higher-order modes are excited at random with a transition probability and are detected by the eavesdropper. Moreover, the secret key sharing cannot be carried out using photons in higher-order modes, because the photons in higher-order modes are rejected by the single-mode fiber in Bob’s station. Therefore, the security of the GI multimode fiber channel is the same as the single-mode fiber channel, except that the additional optical losses caused by the coupling into single-mode fiber in Bob’s station increases bit errors (details of the bit errors are described below).

The performance of our QKD system should be evaluated by use of a quantum-bit-error rate (QBER) given by [11

11 . D. Stucki , N. Gisin , O. Guinnard , G. Ribordy , and H. Zbinden , “ Quantum key distribution over 67 km with a plug and play system ,” New J. Phys. 4 , 41.1 – 41.8 ( 2002 ). [CrossRef]

]

QBER=QBERopt+QBERdark+QBERafter+QBERstray.
(1)

QBERopt for the compatible phase setting is given by [16

16 . H. Zbinden , H. Bechman-Pasquinucci , N. Gisin , and G. Ribordy , “ Quantum cryptography ,” Appl. Phys. B 67 , 743 – 748 ( 1998 ). [CrossRef]

]

QBERopt=CwrongCright+Cwrong,
(2)

where Cright and Cwrong are the correct and false counts subtracting dark counts. Using the data in Fig. 5, we can calculate the mean value over all four possible compatible phase settings. The averaged QBERopt for the 10.5 km spool is 1.23×10-3 and that for the 550 m LAN is 1.46×10-3. On the other hand, QBERdark is given by

QBERdark=(Pdark,1+Pdark,2)2Pphot+Pdark,1+Pdark,2,
(3)

where Pdark,i is the probability of getting a dark count in detector Di, and Pphot is the probability of detecting a photon given by

Pphot=μ2(LD1η1+LD2η2)Li(i=1,2).
(4)

In our QKD experiments performed by randomly changing ϕA and ϕB, the average photon number per pulse μ was set to 0.1. The dark-count probabilities P dark,1 and P dark,2 are 2.2×10-5 and 3.0 × 10-5, respectively. The measured QBERs and bit rates with the values estimated using Eqs. (1)-(4) are summarized in Table 2. The measured QBERs and bit rates are in good agreement with the estimated ones.

5. Conclusions

In conclusion, we have developed a fiber-optic QKD system at 1550 nm based on a polarization-splitting time-multiplexed interferometer incorporating InGaAs/InP single-photon avalanche photodiodes operated in gated mode. Using the system, we have demonstrated QKD over a 550 m installed multimode fiber LAN with a QBER of 1.09 %. Coupling losses between the multimode fiber LAN and the single-mode fiber was reduced by the underfilled mode distribution. Moreover, high fringe visibilities are obtained because of not only the underfilled transmission but also a rejection of higher-order mode by the single-mode fiber in Bob’s station. However, the optical losses at the junction would be large if a number of modes are excited (transition from the underfilled mode distribution to the equivalent mode distributions) in the multimode fiber by extending the LAN. The coupling losses will set a limit to the communication distance in local area QKD using multimode fiber.

References and links

1 .

C. H. Bennett and G. Brassard , “ Quantum cryptography: Public key distribution and coin tossing ,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing ( Institute of Electrical and Electronics Engineers, New York , 1984 ), pp. 175 – 179 .

2 .

C. H. Bennett , F. Bessette , G. Brassard , L. Salvail , and J. Smolin , “ Experimental quantum cryptography ,” J. Crtptol. 5 , 3 – 28 ( 1992 ).

3 .

A. Muller , T. Huttner , W. Tittel , H. Zbinden , and N. Gisin , “ ‘Plug and play’ systems for quantum cryptography ,” Appl. Phys. Lett. 70 , 793 – 795 ( 1997 ). [CrossRef]

4 .

G. Ribordy , J. D. Gautier , N. Gisin , O. Guinnard , and H. Zbinden , “ Automated ‘plug & play’ quantum key distribution ,” Electron. Lett. 34 , 2116 – 2117 ( 1998 ). [CrossRef]

5 .

D. Bethune and W. Risk , “ An autocompensation fiber-optic quantum cryptography system based on polarization splitting of light ,” IEEE J. Quantum Electron. 36 , 340 – 347 ( 2000 ). [CrossRef]

6 .

A. Yoshizawa and H. Tuchida , “ A 1550 nm single-photon detector using a thermoelectrically cooled InGaAs avalanche photodiode ,” Jpn. J. Appl. Phys. Pt. 1 40 , 200 – 201 ( 2001 ). [CrossRef]

7 .

P. Hiskett , G. Bonfrate , G. Buller , and P. Townsend , “ Eighty kilometer transmission experiment using an In-GaAs/InP SPAD-based quantum cryptography receiver operating at 1.55 microns ,” J. Modern Opt. 48 , 1957 – 1966 ( 2001 ).

8 .

D. Stucki , G. Ribordy , A. Stefanov , H. Zbinden , J. G. Rarity , and T. Wall , “ Photon counting for quantum key distribution with Peltier coold InGaAs/InP APD’s ,” J. Modern Opt. 48 , 1967 – 1982 ( 2001 ). [CrossRef]

9 .

N. Namekata , Y. Makino , and S. Inoue , “ Single-photon detector for long-distance fiber optic quantum key distribution ,” Opt. Lett. 27 , 954 – 956 ( 2002 ). [CrossRef]

10 .

H. Kosaka , A. Tomita , Y. Nambu , T. Kimura , and K. Nakamura , “ Single-photon interference experiment over 100 km for quantum cryptography system using a balanced gated-mode photon detector ,” Electron. Lett. 39 , 1199 – 1200 ( 2003 ). [CrossRef]

11 .

D. Stucki , N. Gisin , O. Guinnard , G. Ribordy , and H. Zbinden , “ Quantum key distribution over 67 km with a plug and play system ,” New J. Phys. 4 , 41.1 – 41.8 ( 2002 ). [CrossRef]

12 .

P. D. Townsend , “ Experimental investigation of the performance limits for first telecommunications-window quantum cryptography systems ,” IEEE Photon. Technol. Lett. 10 , 1048 – 1050 ( 1998 ). [CrossRef]

13 .

N. Namekata and S. Inoue , “ Fiber-optic quantum key distribution at 1550 nm ” in Proceedings of the ERATO Workshop on Quantum Information Science (JST, Tokyo, 2002 ), pp. 96 – 97 .

14 .

N. Brunner , V. Scarani , M. Wegmuller , M. Legre , and N. Gisin , “ Direct measurement of superluminal group velocity and signal velocity in an optical fiber ,” Phys. Rev. Lett. 93 , 203902 ( 2004 ). [CrossRef] [PubMed]

15 .

S. Cova , M. Ghioni , A. Lacaita , C. Samori , and F. Zappa , “ Avalanche photodiodes and quenching circuits for single-photon detection ,” Appl. Opt. 35 , 1956 – 1963 ( 1996 ). [CrossRef] [PubMed]

16 .

H. Zbinden , H. Bechman-Pasquinucci , N. Gisin , and G. Ribordy , “ Quantum cryptography ,” Appl. Phys. B 67 , 743 – 748 ( 1998 ). [CrossRef]

OCIS Codes
(030.5260) Coherence and statistical optics : Photon counting
(040.5570) Detectors : Quantum detectors
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(270.0270) Quantum optics : Quantum optics

ToC Category:
Research Papers

Citation
Naoto Namekata, Shigehiko Mori, and Shuichiro Inoue, "Quantum key distribution over an installed multimode optical fiber local area network," Opt. Express 13, 9961-9969 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-9961


Sort:  Journal  |  Reset  

References

  1. C. H. Bennett and G. Brassard, "Quantum cryptography: public key distribution and coin tossing," in Proceedings of IEEE International Conference on computers, systems, and signal processing (IEEE, New York, 1984), pp. 175-179.
  2. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, "Experimental quantum cryptography," J. Cryptology 5, 3-28 (1992).
  3. A. Muller, T. Huttner, W. Tittel, H. Zbinden, and N. Gisin, "Plug and play systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997). [CrossRef]
  4. G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Automated 'plug & play' quantum key distribution," Electron. Lett. 34, 2116-2117 (1998). [CrossRef]
  5. D. Bethune and W. Risk, "An auto compensation fiber-optic quantum cryptography system based on polarization splitting of light," IEEE J. Quantum Electron. 36, 340-347 (2000). [CrossRef]
  6. A. Yoshizawa and H. Tuchida, "A 1550 nm single-photon detector using a thermoelectrically cooled InGaAs avalanche photodiode," Jpn. J. Appl. Phys. Pt. 1 40, 200-201 (2001). [CrossRef]
  7. P. Hiskett, G. Bonfrate, G. Buller, and P. Townsend, "Eighty kilometer transmission experiment using an InGaAs/InP SPAD-based quantum cryptography receiver operating at 1.55 microns," J. Modern Opt. 48, 1957-1966 (2001).
  8. D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APD's," J. Modern Opt. 48, 1967-1982 (2001). [CrossRef]
  9. N. Namekata, Y. Makino, and S. Inoue, "Single-photon detector for long-distance fiber optic quantum key distribution,"Opt. Lett. 27, 954-956 (2002). [CrossRef]
  10. H. Kosaka, A. Tomita, Y. Nambu, T. Kimura, and K. Nakamura, "Single-photon interference experiment over 100 km for quantum cryptography system using a balanced gated-mode photon detector," Electron. Lett. 39, 1199-1200 (2003). [CrossRef]
  11. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, "Quantum key distribution over 67 km with a plug and play system," New J. Phys. 4, 41.1-41.8 (2002). [CrossRef]
  12. . P. D. Townsend, "Experimental investigation of the performance limits for first telecommunications-window quantum cryptography systems," IEEE Photon. Technol. Lett. 10, 1048-1050 (1998). [CrossRef]
  13. N. Namekata and S. Inoue, "Fiber-optic quantum key distribution at 1550 nm," in Proceedings of the ERATO Workshop on Quantum Information Science (JST, Tokyo, 2002), pp. 96-97.
  14. N. Brunner, V. Scarani, M. Wegmuller, M. Legre, and N. Gisin, "Direct measurement of superluminal group velocity and signal velocity in an optical fiber," Phys. Rev. Lett. 93, 203902 (2004). [CrossRef] [PubMed]
  15. S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, "Avalanche photodiodes and quenching circuits for single-photon detection," Appl. Opt. 35, 1956-1963 (1996). [CrossRef] [PubMed]
  16. H. Zbinden, H. Bechman-Pasquinucci, N. Gisin and G. Ribordy, "Quantum cryptography," Appl. Phys. B 67, 743-748 (1998). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited