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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 13 — Jun. 25, 2007
  • pp: 8465–8471
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Practical quantum key distribution over 60 hours at an optical fiber distance of 20km using weak and vacuum decoy pulses for enhanced security

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields  »View Author Affiliations


Optics Express, Vol. 15, Issue 13, pp. 8465-8471 (2007)
http://dx.doi.org/10.1364/OE.15.008465


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Abstract

Experimental one-way decoy pulse quantum key distribution running continuously for 60 hours is demonstrated over a fiber distance of 20km. We employ a decoy protocol which involves one weak decoy pulse and a vacuum pulse. The obtained secret key rate is on average over 10kbps. This is the highest rate reported using this decoy protocol over this fiber distance and duration.

© 2007 Optical Society of America

1. Introduction

Quantum key distribution (QKD) involves the secure communication between two remote parties, conventionally named Alice (sender) and Bob (receiver), where the security of the keys is determined by the laws of quantum mechanics rather than the use of strong, one-way mathematical functions to encrypt the keys [1

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

]. Where security is of paramount importance, QKD naturally would be the technique of choice for secret key distribution owing to its unconditionally secure nature. Although since the original proposal [2

2. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, (IEEE, New York, 1984), pp. 175179.

], there has been a considerable amount of work on QKD, beginning with the first experimental demonstration in 1992 [3

3. C. H. Bennett, F. Bessette, G. Brassard, L. Savail, and J. Smolin, “Experimental quantum cryptography,” J. Cryp-tol. 53–28 (1992).

], reliable, compact systems with tolerably high enough bit rates compatible with existing telecoms fiber technology are only now starting to emerge [4

4. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, “Quantum key distribution over 67km with a plug & play system,” New J. Phys. 441.1–41.8 (2002). [CrossRef]

, 5

5. C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004). [CrossRef]

]. Ideally the QKD setup should be arranged employing a true single photon source to guarantee immunity against the so-called pulse number splitting attacks (PNS)[6

6. X.-B. Wang, “Beating the photon pulse-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503-1–4 (2005) and H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504-1–4 (2005). [CrossRef] [PubMed]

, 7

7. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limits on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000). [CrossRef] [PubMed]

] from a potential eavesdropper (Eve). Presently there are a lack of deterministic, reliable and useful single photon sources. Therefore most implementations rely on heavily attenuated lasers as a photon source which emit photon pulses with a Poissonian number distribution. The PNS attack in such a configuration would consist of blocking any true single photons in the quantum channel, removing part of the multi-photon pulses and transmitting the remaining portion to Bob via a lossless channel. In Eve’s best case scenario, Bob’s detection rate is maintained while Bob is oblivious to Eve’s presence. Eve can then determine all or part of the key [7

7. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limits on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000). [CrossRef] [PubMed]

].

A recent proposal [8

8. W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91, 057901-1–4 (2003). [CrossRef] [PubMed]

] circumvents the PNS attack using additional (decoy) pulses sent by Alice. These pulses in general have different pulses intensities compared to the signal pulses and are interleaved randomly with the signal pulses. Bob measures the transmittances of the quantum channel for these different pulse intensities and can then infer tighter bounds on the final secure key by the ability to detect PNS attacks. Under such conditions Eve is powerless to attack the channel using the PNS. Recently a proof of the decoy pulse protocol has been displayed (GLLP)[9

9. D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quant. Inf. Comp. 5, 325–360 (2004).

] which also includes realistic (if pessimistic) experimental assumptions; Bob’s detectors can be manipulated by Eve and the detectors have finite detection efficiency. A recent experimental bi-directional decoy pulse system has been implemented [10

10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502-1–4 (2006). [CrossRef] [PubMed]

] but (as pointed out by Ref. [10

10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502-1–4 (2006). [CrossRef] [PubMed]

]) a drawback of bi-directional systems are the pulse intensities can indeed be tampered with by Eve unknown to Alice and Bob, thus compromising security. Very recently we showed an extremely promising one-way QKD system employing a single decoy pulse [11

11. Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “Unconditionally secure one-way quantum key distribution using decoy pulses,” Appl. Phys. Lett. 90, 011118-1–3 (2007). [CrossRef]

]. This system displayed a high key rate of over 5kbps with 25km of optical fiber. For a non-decoy system using much quieter detectors a secure bit rate of just 43bps was achieved over the same length of fiber [12

12. C. Gobby, Z. L. Yuan, and A. J. Shields, Elec. Lett. “Unconditionally secure quantum key distribution over 50 km of standard telecom fiber,” Electron. Lett. 40, 1603–1605 (2004). [CrossRef]

]. This illustrates the power of the decoy pulse method in providing a much more stringent bound on the security of the final key. Even tighter bounds can be achieved using more than one decoy pulse [6

6. X.-B. Wang, “Beating the photon pulse-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503-1–4 (2005) and H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504-1–4 (2005). [CrossRef] [PubMed]

]. Theory shows that it is usually enough to limit the number of decoy pulses to two decoy pulses only. The optimal case for the two decoy pulses is for one decoy of which is a lower intensity ν than the signal pulse μ and another which has an intensity close to zero or “vacuum-like” [13

13. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012306-1–15 (2005). [CrossRef]

]. The lower bound on the single photon gain,

Fig. 1. Schematic of the optical layout of the one-way quantum key distribution system. The system employs BB84 phase encoding and the weak + vacuum decoy protocol. Attn: attenuator, IM: intensity modulator, PC: polarization controller, WDM: wavelength division multiplexer, FS: fiber stretcher. The QKD optics are driven by field programmable gate arrays (FPGAs) electronics. Fast (MHz) electronic pulse routes: solid arrows; slow (Hz) electronic pulse routes: dotted arrows.

QL 1 is then given by three transmittances, signal, decoy and vacuum respectively: Qμ, Qν and Y 0 [13

13. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012306-1–15 (2005). [CrossRef]

, 10

10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502-1–4 (2006). [CrossRef] [PubMed]

]:

Q1L=μ2ν2μ2μν{QνLeνQνeμν2μ2Y0Uμ2ν2μ2}
(1)

where QνL (YU 0) are the lower (upper) bounds on the decoy pulse and vacuum transmittances respectively , estimated conservatively as ten standard deviations of Qν (Y 0) from the measured value ensuring a confidence interval of 1 - 1.5 × 10-23. The bit errors are assumed to derive from the subset of single photon pulses and the upper bound for the single photon error rate can be written as:

ε1U=εμQμQ1LY0LeμQ1L
(2)

where εμ is the signal error rate and YL 0 is the lower bound on the vacuum transmittance (estimated as as ten standard deviations of Y 0 from the measured value). The lower bound on the final secure key rate, RL can then be determined by the following expression:

RRL=qNμ{Qμf(εμ)H2(εμ)+Q1L(1H2(ε1U))}t
(3)

where q = 0.5 for the BB84 protocol, Nμ is the total number of signal pulses sent by Alice, f(x) is the bi-directional error correction efficiency above the Shannon limit is estimated to be f(εμ) ∼ 1.10, H 2 = -xlog2(x)-(1-x)log2(1-x) is the binary entropy function and the time t is the duration of the key session. The first term in eq. (3) corresponds to error correction; the second term corresponds to the single photon gain modified by privacy amplification (H 2(εU 1)). Although the weak + vacuum decoy protocol is predicted to have an improved performance over the single decoy pulse protocol, recent implementations [14

14. C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-Xin. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505-1–4 (2007). [CrossRef] [PubMed]

, 15

15. D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita , S-W. Nam, and J. E. Nordholt, “Long-distance decoy-State quantum key distribution in optical fiber,” Phys. Rev. Lett. 98, 010505-1–4 (2007). [CrossRef]

] show relatively low key generation rates and are limited to local synchronization.

Here we present a one-way weak + vacuum decoy pulse system which has a relatively high secure continuous key rate of more than 10kbps over 20km of fiber length. The key generation rate is stable over the rate time period of 60 hours and the system requires no manual alignment for set-up or during operation.

Fig. 2. Experimentally measured data for the 60 hours experiment. (a)Transmittances of the signal, decoy and vacuum. (b) The quantum bit error rates of the the signal (Eμ) and the non-zero decoy (Eν) as a function of time.

2. QKD experimental setup

We use a one-way fiber optic QKD system with phase encoding as shown in Fig. 1. Two Mach-Zehnder phase encoding interferometers are employed for the phase encoding (Alice; sender) and decoding (Bob; receiver). Alice and Bob have a 20km fiber spool linking them through which the signal (λ = 1.55μm) and clock (λ = 1.3μm) optical pulses are transmitted. The 1.3μm clock pulse duration is 5ns with a peak intensity of ∼ 5μW; average intensity is ∼ 200nW at Alice. The clock pulse over the entire transmission distance does not overlap the (1.55μm) signal pulses. The signal laser is a distributed feedback type and emits a fixed intensity train of pulses at a repetition rate of 7.143MHz. An intensity modulator is used to produce signal and decoy pulses of differing intensities. The vacuum decoy pulse is produced by omitting trigger pulses to the signal laser. All signal, decoy and vacuum pulses are produced at random times and can have relative occurance probabilities assigned to them. The signal and decoy pulses are attenuated strongly to the single photon level after which a much stronger clock pulse is wavelength division multiplexed with them to provide synchronization between Alice and Bob’s electronics. Customized electronics based on FPGAs were developed in house to drive the QKD optics. An active stabilization technique is employed to ensure continuously running operation. Bob’s detectors are two single photon InGaAs avalanche photodiodes (APDs) cooled to approximately -30°C and characterized to have negligible afterpulsing [16

16. G. Ribordy, J. D. Gautier, H. Zbinden, and N. Gisin, “Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters,” Appl. Opt. 37, 2272 (1998). [CrossRef]

]. . Their combined dark count rates are ∼ 1.4 × 10-4. Bob’s detector efficiency ∼ 10% and loss ∼ 2.5dB gives rise to an overall efficiency of 5.62 × 10-2. The weak + vacuum including BB84 protocol was implemented. Numerical simulation to maximize the secure bit rate was performed to yield the optimal intensities of the signal and decoy pulses as μ = 0.55 and ν = 0.098. Numerical simulation also provided the optimal probabilities of pulses: signal Nμ = 0.93, decoy pulse Nν = 0.062 and vacuum pulse N 0 = 0.016. The session length for each QKD key is selected as 3 × 106 bits which corresponds to roughly 6 × 106 detection events by Bob. A total of 3262 sessions were distributed with an average individual session time of ∼ 71 seconds.

Fig. 3. The final secure bit rate as a function of time. The extremely long term drift in the key rate is attributed to long term day to day temperature drift in the laboratory. Inset: distribution of the secure bit rates for the keys.

3. Results

Figure 2(a) shows the experimentally measured transmittances of the signal, decoy and vacuum pulses. The values are stable and constant over the duration of the experiment and agree well with the theoretically predicted transmittance (per pulse): Qμ = 0.01270±0.00078, Qν = 0.00234±0.00014 where the errors are two standard deviations; for the vacuum transmittance (per pulse), Y 0 = 1.34±0.20 × 10-4 in good agreement with the measured dark count value of ∼ 1.4 × 10-4 measured prior to the experiment. A small (simultaneous) proportion of fluctuations in Qμ and Qν are observed and are attributed to polarization and/or fiber stretcher resets during which photons were temporarily not counted. These obtained transmittances indicates the various optical states had been well prepared and detected. The associated quantum bit error rates of both the signal (Eμ) and the non-zero decoy (Eν) are plotted in Fig. 2(b). They are fairly stable and constant. The final secure bit rate is displayed in Fig. 3. A secure bit rate of > 10kbps is observed. The long term drift in the key rate is attributed to long term temperature drift from day through to night (the period is roughly 24 hours) in the laboratory affecting the overall temperature of the 20km fiber spool. In a real world environment the fiber is usually located around 1 meter underground leading to very stable fiber temperatures. This would eliminate this long term drift observed here.

The bit rate of > 10kbps is approximately more than two orders of magnitude higher than what can be achieved at a fiber distance of 20km without decoy states [12

12. C. Gobby, Z. L. Yuan, and A. J. Shields, Elec. Lett. “Unconditionally secure quantum key distribution over 50 km of standard telecom fiber,” Electron. Lett. 40, 1603–1605 (2004). [CrossRef]

]. Indeed, if one were to employ more decoy states than the two we use here, there is not that much advantage to be gained. As shown in [13

13. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012306-1–15 (2005). [CrossRef]

] the secure bit rate as a function of fiber distance for the single pulse and dual decoy pulse protocols varies significantly. However, the weak plus vacuum protocol is close to the asymptotic limit of using an infinite number of decoy states. This can be understood intuitively by the fact that the photon distribution is Poissonian and states with a photon number N > 2 have a very small probability of occurring. Hence they will contribute little to the overall photon distribution when the average photon numbers of the signal and decoy states are μ,ν < 1. Additionally, there are practical problems in using more decoy pulses such as a decrease of duty cycle of signal pulses, greater requirements on Alices’ random number generator and more data processing power needed.

The possibility of nonlinear effects being generated in the fiber due to the clock and signal pulses is negligible on the results of the quantum key distribution. As stated previously, both clock and signal pulses never overlap in time throughout the entire transmission rendering possible mixing effects negligible. Addtionally, any (small) Raman scattering generated by the clock pluse in the fiber was adequately filtered out using an efficient wavelength division multiplexer at Bob. In any case, if the Raman scattering was a problem, the quantum bit error rate would be higher than observed. Finally, the experimentally observed quantum transmittances agrees very well with the predicted transmittances indicating the system performs with the expected losses accurately.

Fig. 4. (a)(i) Frequency count distribution of the quantum transmittance ratio Qν/Qμ. (ii) The secure bit rate simulated as a function of Qν/Qμ (solid line); experimentally measured data (red crosses). (b)(i) Frequency count distribution of the vacuum count probability Y 0. (ii) The secure bit rate as a function of Y 0 (solid black line); experimentally measured data (red crosses). Also shown for comparison is the single decoy protocol secure bit rate (dotted line). The dotted lines in both Figs. show the expected values in the absence of PNS attacks, artifacts and manipulations of the vacuum count rates.

To assess the possibility of a PNS attack on the key distribution, the technique used previously [11

11. Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “Unconditionally secure one-way quantum key distribution using decoy pulses,” Appl. Phys. Lett. 90, 011118-1–3 (2007). [CrossRef]

] was to monitor the ratio of transmittances Qν/Qμ. If Eve decides to implement a PNS attack, the ratio Qν/Qμ will dip below the expected value as preferentially more multi-photon signals would be transmitted to Bob (the transmittance Qμ > Qν due to μ > ν). This is displayed in Fig. 4(a)(ii). No secure bit rate is possible with Qν/Qμ < 0.13.

Now with an additional vacuum pulse at our disposal we can also check for Eve’s manipulation of the vacuum rates. In keeping with the paranoid assumptions of GLLP [9

9. D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quant. Inf. Comp. 5, 325–360 (2004).

], we assume Eve can either reduce or increase the vacuum rates. Depicted in Fig. 4(b)(ii) is the simulated effect of changing Y 0 on the secure bit rate. For the weak plus vacuum protocol implemented here no secure bit rate is possible for Y 0 > 10-3 (solid black line). However, if one were to use a single (non-vacuum) decoy protocol (dotted blue line) no secure bit rate would be possible for Y 0 > 4.8×10-4. This shows the power of using more than one decoy pulse. Further insight can be gained by examining the formulae for the weak plus vacuum protocol (eq.(1) & eq.(2)). The magnitudes of the single photon gain (privacy amplification) are greater (smaller) respectively by using the weak + vacuum protocol compared to employing the single pulse protocol. This is manifest through a tighter bound on the single photon gain eq. (1) and the single photon error rate eq. (2). The second term in eq. (2) reduces the overall single photon error rate due to the measurement of the vacuum pulses. In the single decoy pulse protocol this term is zero.

Finally we address the issue of the small number of spikes observed in the vacuum counts transmittance (Fig. 2(a)). All classical messages are exchanged on the internet. We believe the spiking is due to increased internet traffic slowing down classical exchange of information between Alice and Bob and thereby affecting synchronization. It affected less than 1% of the entire set of quantum keys exchanged over the 60 hour period. For large numbers of counts (the signal and decoy pulses) this effect is small, but for low numbers of counts (Y 0) this effect can be apparent. We are currently working to improve this problem with modifications to the software. However, we note this behaviour does not compromise security as evident from Fig. 4(b)(ii). As can be seen, an increase in Y 0 overestimates the amount of privacy amplification and results in a shorter key, hence lower final secure key rate. The final secure key rate is underestimated for this small fraction of keys.

4. Conclusions

Acknowledgements

The authors would like to thank the EC for funding under the FP6 Integrated Project SECOQC.

References and links

1.

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

2.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, (IEEE, New York, 1984), pp. 175179.

3.

C. H. Bennett, F. Bessette, G. Brassard, L. Savail, and J. Smolin, “Experimental quantum cryptography,” J. Cryp-tol. 53–28 (1992).

4.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, “Quantum key distribution over 67km with a plug & play system,” New J. Phys. 441.1–41.8 (2002). [CrossRef]

5.

C. Gobby, Z. L. Yuan, and A. J. Shields, “Quantum key distribution over 122km of standard telecom fiber,” Appl. Phys. Lett. 84, 3762–3764 (2004). [CrossRef]

6.

X.-B. Wang, “Beating the photon pulse-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503-1–4 (2005) and H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504-1–4 (2005). [CrossRef] [PubMed]

7.

G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limits on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000). [CrossRef] [PubMed]

8.

W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91, 057901-1–4 (2003). [CrossRef] [PubMed]

9.

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quant. Inf. Comp. 5, 325–360 (2004).

10.

Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, “Experimental quantum key distribution with decoy states,” Phys. Rev. Lett. 96, 070502-1–4 (2006). [CrossRef] [PubMed]

11.

Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “Unconditionally secure one-way quantum key distribution using decoy pulses,” Appl. Phys. Lett. 90, 011118-1–3 (2007). [CrossRef]

12.

C. Gobby, Z. L. Yuan, and A. J. Shields, Elec. Lett. “Unconditionally secure quantum key distribution over 50 km of standard telecom fiber,” Electron. Lett. 40, 1603–1605 (2004). [CrossRef]

13.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012306-1–15 (2005). [CrossRef]

14.

C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-Xin. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98, 010505-1–4 (2007). [CrossRef] [PubMed]

15.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita , S-W. Nam, and J. E. Nordholt, “Long-distance decoy-State quantum key distribution in optical fiber,” Phys. Rev. Lett. 98, 010505-1–4 (2007). [CrossRef]

16.

G. Ribordy, J. D. Gautier, H. Zbinden, and N. Gisin, “Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters,” Appl. Opt. 37, 2272 (1998). [CrossRef]

17.

M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with decoy method,” quant-ph/0702250 (2007).

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(270.0270) Quantum optics : Quantum optics
(270.5290) Quantum optics : Photon statistics

ToC Category:
Quantum Optics

History
Original Manuscript: May 4, 2007
Revised Manuscript: June 15, 2007
Manuscript Accepted: June 18, 2007
Published: June 22, 2007

Citation
J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, "Practical quantum key distribution over 60 hours at an optical fiber distance of 20km using weak and vacuum decoy pulses for enhanced security," Opt. Express 15, 8465-8471 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8465


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References

  1. N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
  2. C. H. Bennett and G. Brassard, "Quantum cryptography: public key distribution and coin tossing," in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, (IEEE, New York, 1984), pp. 175179.
  3. C. H. Bennett, F. Bessette, G. Brassard, L. Savail and J. Smolin, "Experimental quantum cryptography," J. Cryptol. 53-28 (1992).
  4. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy and H. Zbinden, "Quantum key distribution over 67km with a plug & play system," New J. Phys. 4 41.1-41.8 (2002). [CrossRef]
  5. C. Gobby, Z. L. Yuan and A. J. Shields, "Quantum key distribution over 122km of standard telecom fiber," Appl. Phys. Lett. 84, 3762-3764 (2004). [CrossRef]
  6. X.-B. Wang, "Beating the photon pulse-number-splitting attack in practical quantum cryptography," Phys. Rev. Lett. 94, 230503-1-4 (2005) and H.-K. Lo, X. Ma and K. Chen, "Decoy state quantum key distribution," Phys. Rev. Lett. 94, 230504-1-4 (2005). [CrossRef] [PubMed]
  7. G. Brassard, N. L¨utkenhaus, T. Mor and B. C. Sanders, "Limits on practical quantum cryptography," Phys. Rev. Lett. 85, 1330-1333 (2000). [CrossRef] [PubMed]
  8. W.-Y. Hwang, "Quantum key distribution with high loss: toward global secure communication," Phys. Rev. Lett. 91, 057901-1-4 (2003). [CrossRef] [PubMed]
  9. D. Gottesman, H.-K. Lo, N. Lutkenhaus and J. Preskill, "Security of quantum key distribution with imperfect devices," Quant. Inf. Comp. 5, 325-360 (2004).
  10. Y. Zhao, B. Qi, X. Ma, H.-K. Lo and L. Qian, "Experimental quantum key distribution with decoy states," Phys. Rev. Lett. 96, 070502-1-4 (2006). [CrossRef] [PubMed]
  11. Z. L. Yuan, A. W. Sharpe and A. J. Shields, "Unconditionally secure one-way quantum key distribution using decoy pulses," Appl. Phys. Lett. 90, 011118-1-3 (2007). [CrossRef]
  12. C. Gobby, Z. L. Yuan and A. J. Shields, Elec. Lett. "Unconditionally secure quantum key distribution over 50 km of standard telecom fiber," Electron. Lett. 40, 1603-1605 (2004). [CrossRef]
  13. X. Ma, B. Qi, Y. Zhao and H.-K. Lo, "Practical decoy state for quantum key distribution," Phys. Rev. A 72, 012306-1-15 (2005). [CrossRef]
  14. C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-Xin. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang and J.-W. Pan, "Experimental long-distance decoy-state quantum key distribution based on polarization encoding," Phys. Rev. Lett. 98, 010505-1-4 (2007). [CrossRef] [PubMed]
  15. D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S-W. Nam and J. E. Nordholt, "Long-distance decoy-State quantum key distribution in optical fiber," Phys. Rev. Lett. 98, 010505-1-4 (2007). [CrossRef]
  16. G. Ribordy, J. D. Gautier, H. Zbinden, and N. Gisin, "Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters," Appl. Opt. 37, 2272 (1998). [CrossRef]
  17. M. Hayashi, "Upper bounds of eavesdropper’s performances in finite-length code with decoy method," quantph/ 0702250 (2007).

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