## Entangled quantum key distribution over two free-space optical links

Optics Express, Vol. 16, Issue 21, pp. 16840-16853 (2008)

http://dx.doi.org/10.1364/OE.16.016840

Acrobat PDF (2768 KB)

### Abstract

We report on the first real-time implementation of a quantum key distribution (QKD) system using entangled photon pairs that are sent over two free-space optical telescope links. The entangled photon pairs are produced with a type-II spontaneous parametric down-conversion source placed in a central, potentially untrusted, location. The two free-space links cover a distance of 435 m and 1,325 m respectively, producing a total separation of 1,575 m. The system relies on passive polarization analysis units, GPS timing receivers for synchronization, and custom written software to perform the complete QKD protocol including error correction and privacy amplification. Over 6.5 hours during the night, we observed an average raw key generation rate of 565 bits/s, an average quantum bit error rate (QBER) of 4.92%, and an average secure key generation rate of 85 bits/s.

© 2008 Optical Society of America

## 1. Introduction

1. S. Wiesner, “Conjugate Coding,” Sigact News **15**, 78–88 (1983). [CrossRef]

2. C. H. Bennett and G. Brassard, in *Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing* , (New York, 1984) p. 175. [PubMed]

*et al*. [3

3. K. Resch, M. Lindenthal, B. Blauensteiner, H. Bohm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderback, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing Entanglement and Single Photons Through an Intra-City Free-Space Quantum Channel,” Opt. Exp. **13**, 202 (2005). [CrossRef]

*et al*. [4

4. C. Peng, T. Yang, X. Bao, J. Zhang, X. Jin, F. Feng, B. Yang, J. Yang, J. Yin, Q. Zhiang, N. Li, B. Tian, and J.W. Pan, “Experimental Free-Space Distribution of Entangled Photon pairs Over 13km: Towards Satellite-Based Global Quantum Communication,” Phys. Rev. Lett. **94**, 150501 (2005) [CrossRef] [PubMed]

*et al*. [5

5. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-Based Quantum Communication Over 144km,” Nat. Phys. **3**, 481–486 (2007). [CrossRef]

*et al*. [6

6. I. Marcikic, A. Lamas-Linares, and C. Kurtsiefer, “Free-Space Quantum Key Distribution with Entangled Photons,” Appl. Phys. Lett. **89**, 101122 (2006). [CrossRef]

*et al*. [7

7. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “A Framework for Practical Quantum Cryptography,” http://arxiv.org/abs/0802.4155 (2008).

8. J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to Satellite Secure Key Exchange Using Quantum Cryptography,” New J. Phys. **4**, 82 (2002). [CrossRef]

9. M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron **9**, 1541 (2003). [CrossRef]

10. J. Perdigues, B. Furch, C. de Matos, O. Minster, L. Cacciapuoti, M. Pfennigbauer, M. Aspelmeyer, T. Jennewein, R. Ursin, T. Schmitt-Manderbach, G. Baister, J. Rarity, W. Leeb, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Quantum Communications at ESA - Towards a Space Experiment on the ISS,” in *58th International Astronautical Congress* (Hyderabad, India, 2007).

## 2. Security assumptions

7. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “A Framework for Practical Quantum Cryptography,” http://arxiv.org/abs/0802.4155 (2008).

11. R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC White Paper on Quantum Key Distribution and Cryptography,” http://arxiv.org/abs/quant-ph/0701168 (2007).

*et al*. [14

14. X. Ma, C. H. Fung, and H. K. Lo, “Quantum Key Distribution With Entangled Photon Sources,” http://arxiv.org/abs/quant-ph/0703122 (2007).

16. N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing Models for Optical Measurements in Quantum Communication,” http://arxiv.org/abs/0804.3082 (2008).

17. T. Tsurumaru and K. Tamaki, “Security Proof for QKD Systems with Threshold Detectors,” http://arxiv.org/abs/0803.4226 (2008).

18. M. Koashi, Y. Adachi, T. Yamamoto, and N. Imoto, “Security of Entanglement-Based Quantum Key Distribution with Practical Detectors,” http://arxiv.org/abs/0804.0891 (2008).

15. J. Hasegawa, M. Hayashi, T. Hiroshima, A. Tanaka, and A. Tomita, “Experimental Decoy State Quantum Key Distribution with Unconditional Security Incorporating Finite Statistics,” http://arxiv.org/abs/0705.3081 (2007).

## 3. Experimental implementation

*et al*. [20

20. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum Cryptography without Bell’s Theorem,” Phys. Rev. Lett. **68**, 557 (1992). [CrossRef] [PubMed]

24. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. **75**, 4337 (1995). [CrossRef] [PubMed]

*µ*m in a 1 mm thick

*β*-BBO crystal. The down-converted photon pairs at a degenerate wavelength of 815 nm are split off via two small prism mirrors. An achromatic doublet lens (f=150 mm) collimates the down-converted photons and a half waveplate oriented at 45 ° plus a 0.5mm

*β*-BBO crystal in each arm compensate for longitudinal and transverse walk-off effects. The angle of one of the compensator crystals is also used to set the relative phase between horizontal and vertical polarizations in order to produce the singlet Bell state. After compensation, the photons are coupled into short singlemode optical fibers using aspheric lenses (f=11 mm), which can then be coupled either to long singlemode fibers which will carry the photons to the sending telescopes or to local detectors. The fibers pass through manual polarization controllers which are used to undo the polarization rotation induced by the singlemode fibers.

^{-1}and total single photon count rates on each side of 100,000 s

^{-1}. The local entanglement quality is ascertained by measuring the visibility of the source in the rectilinear (H/V) basis and the diagonal (+45°/-45°) basis. For the experimental run detailed in this article we measured visibilities of 99.6% and 91% respectively shortly before the start of the experiment. This corresponds to a local QBER of 2.35%. The limited visibility in the diagonal basis is likely due to the broad spectral filtering (10 nm) and uncompensated transverse walk-off in the

*β*-BBO crystal which is aggravated by the narrow pump beam spot.

*β*-BBO crystal, entangled photon pairs correspond to simultaneous detection events after path length differences are taken into account. Accepting only simultaneous detections reduces the background almost to zero. However, this requirement currently forces us to experiment at night, since the background detection rates experienced during the day both overload our photon detectors and make entangled photon identification with this method infeasible.

25. NIST, “NIST Timing Software,” http://tf.nist.gov/service/its.htm (2008).

14. X. Ma, C. H. Fung, and H. K. Lo, “Quantum Key Distribution With Entangled Photon Sources,” http://arxiv.org/abs/quant-ph/0703122 (2007).

*N*

_{secure}is the final number of secure bits which Alice and Bob will have after privacy amplification,

*N*

_{raw}is the number of bits after error correction,

*h*

_{2}(

*x*)=-

*x*log

*x*-(1-

*x*)log(1-

*x*) is the binary entropy function,

*N*

_{leakage}is the number of bits revealed during error correction, and

*N*

_{safety}is an additional safety parameter, which we set to 30 bits in our experiments. Using this reduction ensures that our system is secure both against symmetric individual attacks (QBER <14.6%) and coherent attacks (QBER <11%); generating no key if the QBER rises above 11%. Note that it is possible to achieve secure key distribution with QBER’s above 11% but it requires the use of two-way classical post-processing which we do not perform in our system. Thus, the upper limit of secure key generation for our system is a QBER of 11%.

27. J. L. Carter and M. N. Wegman, “Universal Classes of Hash Functions,” J. Comput. Syst. Sci. **18**, 143 (1979). [CrossRef]

## 4. Results

^{-1}which varied wildly due to the beam fluctuation over the PI link. Figure 3 shows the quantum bit error rate (QBER) observed over the course of the experiment from 11:55 pm until 6:15 am at which point the rising sun saturated our detectors and made correct coincidence detection impossible due to the high background. This caused the QBER to skyrocket and prevented further secure key generation. The contributions to the total QBER from both X and Z errors are also shown. The total average QBER during the experiment was observed to be 4.92% of which 2.11% and 2.81% were X and Z errors respectively. The increase in the QBER from the baseline 3.85% expected to the observed 4.92% is due to residual uncompensated birefringence in the singlemode fiber used to transport the photons from the source to the sender telescopes and to accidental coincidences.

14. X. Ma, C. H. Fung, and H. K. Lo, “Quantum Key Distribution With Entangled Photon Sources,” http://arxiv.org/abs/quant-ph/0703122 (2007).

*a priori*probabilities of having a 0 or 1 in the raw key. We treat Alice’s raw key as the correct one and assume that Bob is correcting his raw key during the error correction step to match Alice’s. Thus, it is the

*a priori*probabilities of Alice ending up with a 0 or 1 in her rawkey that we are interested in. We calculated Alice’s

*a priori*probabilities of getting a 0 or 1 according to Eq. 3, where

*N*

_{0}/1 is the number of 0’s/1’s measured over the course of the experiment which can be computed from the last line in Table 2.

*p*

_{0}=0.4725 and

*p*

_{1}=0.5275. In order to take care of this imbalance during privacy amplification, we would then have to add a term to Eq. 1 so that it becomes Eq. 4, where the

*h*

_{2}(

*p*

_{0}) term is the extra information leaked by the unequal

*a priori*probabilities of Alice getting a 0 or 1.

*h*

_{2}(

*p*

_{0}) or

*h*

_{2}(

*p*

_{1}) in Eq. 4. Computing the extra term for our experiment we find that as a first estimate we would have to shrink the final key size by an additional 0.22% to compensate for the unequal

*a*

*priori*probabilities.

^{-3}residual errors per bit with 8,150 errorless blocks from a total of 9,564 blocks. The somewhat high residual error rate was due to a number of reasons. Simplifications were made in our implementation of the cascade error correction algorithm; namely, rather than going back through all previous passes of cascade the algorithm instead only went back to the first pass. This reduced the effectiveness of our error correction algorithm; however, this was not the dominant source of error since it has been shown that two passes of cascade are usually enough to remove the majority of errors between two bit strings [28]. The dominant source of residual error was due to using the error rate estimate, performed by publically revealing 10% of the sifted key, in order to determine the proper block size for the cascade algorithm. The relatively small sample sizes caused large statistical fluctuations in the error rate estimate leading to a poor choice of the block sizes used in cascade. Improper block sizes in cascade can strongly reduce its effectiveness and were the major source of error in our error correction algorithm. Also, cascade is optimized to work on blocks with errors spread uniformly throughout, in order to accomplish this the sifted key should be randomized before performing cascade on it. Once cascade is properly implemented with efficient block sizes and sifted key randomization the residual error rate can be set to any desired level dependent upon the number of passes performed with cascade.

## 5. Conclusion

## Acknowledgments

## References and links

1. | S. Wiesner, “Conjugate Coding,” Sigact News |

2. | C. H. Bennett and G. Brassard, in |

3. | K. Resch, M. Lindenthal, B. Blauensteiner, H. Bohm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderback, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing Entanglement and Single Photons Through an Intra-City Free-Space Quantum Channel,” Opt. Exp. |

4. | C. Peng, T. Yang, X. Bao, J. Zhang, X. Jin, F. Feng, B. Yang, J. Yang, J. Yin, Q. Zhiang, N. Li, B. Tian, and J.W. Pan, “Experimental Free-Space Distribution of Entangled Photon pairs Over 13km: Towards Satellite-Based Global Quantum Communication,” Phys. Rev. Lett. |

5. | R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-Based Quantum Communication Over 144km,” Nat. Phys. |

6. | I. Marcikic, A. Lamas-Linares, and C. Kurtsiefer, “Free-Space Quantum Key Distribution with Entangled Photons,” Appl. Phys. Lett. |

7. | V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “A Framework for Practical Quantum Cryptography,” http://arxiv.org/abs/0802.4155 (2008). |

8. | J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to Satellite Secure Key Exchange Using Quantum Cryptography,” New J. Phys. |

9. | M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, “Long-Distance Quantum Communication With Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron |

10. | J. Perdigues, B. Furch, C. de Matos, O. Minster, L. Cacciapuoti, M. Pfennigbauer, M. Aspelmeyer, T. Jennewein, R. Ursin, T. Schmitt-Manderbach, G. Baister, J. Rarity, W. Leeb, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Quantum Communications at ESA - Towards a Space Experiment on the ISS,” in |

11. | R. Alléaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. Länger, A. Leverrier, N. Lütkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, “SECOQC White Paper on Quantum Key Distribution and Cryptography,” http://arxiv.org/abs/quant-ph/0701168 (2007). |

12. | B. Qi, C. H. Fung, H. K. Lo, and X. Ma, “Time-Shift Attack in Practical Quantum Cryptosystems,” Quant. Info. Comput. |

13. | X. Ma and H. K. Lo, Centre for Quantum Information and Quantum Control, University of Toronto, 10 King’s College Road, Toronto, ON, M5S 3G4, Canada, (personal communication, 2008). |

14. | X. Ma, C. H. Fung, and H. K. Lo, “Quantum Key Distribution With Entangled Photon Sources,” http://arxiv.org/abs/quant-ph/0703122 (2007). |

15. | J. Hasegawa, M. Hayashi, T. Hiroshima, A. Tanaka, and A. Tomita, “Experimental Decoy State Quantum Key Distribution with Unconditional Security Incorporating Finite Statistics,” http://arxiv.org/abs/0705.3081 (2007). |

16. | N. J. Beaudry, T. Moroder, and N. Lütkenhaus, “Squashing Models for Optical Measurements in Quantum Communication,” http://arxiv.org/abs/0804.3082 (2008). |

17. | T. Tsurumaru and K. Tamaki, “Security Proof for QKD Systems with Threshold Detectors,” http://arxiv.org/abs/0803.4226 (2008). |

18. | M. Koashi, Y. Adachi, T. Yamamoto, and N. Imoto, “Security of Entanglement-Based Quantum Key Distribution with Practical Detectors,” http://arxiv.org/abs/0804.0891 (2008). |

19. | N. Lütkenhaus, Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada, (personal communication, 2008). |

20. | C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum Cryptography without Bell’s Theorem,” Phys. Rev. Lett. |

21. | For more complete details about the system please refer to [22] and [23]. |

22. | C. Erven, “On Free Space Quantum Key Distribution and its Implementation with a Polarization-Entangled Parametric Down Conversion Source,” Master’s thesis, University of Waterloo (2007). |

23. | G. Weihs and C. Erven, “Entangled Free-Space Quantum Key Distribution,” Proc. SPIE |

24. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. |

25. | NIST, “NIST Timing Software,” http://tf.nist.gov/service/its.htm (2008). |

26. | G. Brassard and L. Salvail, “Secret-Key Reconciliation by Public Discussion,” Lect. Notes Comput. Sci. |

27. | J. L. Carter and M. N. Wegman, “Universal Classes of Hash Functions,” J. Comput. Syst. Sci. |

28. | T. Sugimoto and K. Yamazaki, “A Study on Secret Key Reconciliation Protocol”Cascade,” IEICE Trans. Fundamentals |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(270.0270) Quantum optics : Quantum optics

(200.2605) Optics in computing : Free-space optical communication

(270.5565) Quantum optics : Quantum communications

(270.5568) Quantum optics : Quantum cryptography

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 15, 2008

Revised Manuscript: September 15, 2008

Manuscript Accepted: September 30, 2008

Published: October 7, 2008

**Citation**

C. Erven, C. Couteau, R. Laflamme, and G. Weihs, "Entangled quantum key distribution
over two free-space optical links," Opt. Express **16**, 16840-16853 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16840

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### References

- S. Wiesner, "Conjugate Coding," Sigact News 15, 78-88 (1983). [CrossRef]
- C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, (New York, 1984) p. 175. [PubMed]
- K. Resch, M. Lindenthal, B. Blauensteiner, H. Bohm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderback, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, "Distributing Entanglement and Single Photons Through an Intra-City Free-Space Quantum Channel," Opt. Exp. 13, 202 (2005). [CrossRef]
- C. Peng, T. Yang, X. Bao, J. Zhang, X. Jin, F. Feng, B. Yang, J. Yang, J. Yin, Q. Zhiang, N. Li, B. Tian, and J. W. Pan, "Experimental Free-Space Distribution of Entangled Photon pairs Over 13km: Towards Satellite-Based Global Quantum Communication," Phys. Rev. Lett. 94, 150501 (2005) [CrossRef] [PubMed]
- R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Furst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, "Entanglement-Based Quantum Communication Over 144km," Nat. Phys. 3, 481-486 (2007). [CrossRef]
- I. Marcikic, A. Lamas-Linares, and C. Kurtsiefer, "Free-Space Quantum Key Distribution with Entangled Photons," Appl. Phys. Lett. 89, 101122 (2006). [CrossRef]
- V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, N. Lutkenhaus, and M. Peev, "A Framework for Practical Quantum Cryptography," http://arxiv.org/abs/0802.4155 (2008).
- J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, "Ground to Satellite Secure Key Exchange using Quantum Cryptography," New J. Phys. 4, 82 (2002). [CrossRef]
- M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger, "Long-Distance Quantum Communication With Entangled Photons Using Satellites," IEEE J. Sel. Top. Quantum Electron 9, 1541 (2003). [CrossRef]
- J. Perdigues, B. Furch, C. de Matos, O. Minster, L. Cacciapuoti, M. Pfennigbauer, M. Aspelmeyer, T. Jennewein, R. Ursin, T. Schmitt-Manderbach, G. Baister, J. Rarity, W. Leeb, C. Barbieri, H. Weinfurter, and A. Zeilinger, "Quantum Communications at ESA - Towards a Space Experiment on the ISS," in 58th International Astronautical Congress (Hyderabad, India, 2007).
- R. All�??eaume, J. Bouda, C. Branciard, T. Debuisschert, M. Dianati, N. Gisin, M. Godfrey, P. Grangier, T. L¨anger, A. Leverrier, N. L¨utkenhaus, P. Painchault, M. Peev, A. Poppe, T. Pornin, J. Rarity, R. Renner, G. Ribordy, M. Riguidel, L. Salvail, A. Shields, H. Weinfurter, and A. Zeilinger, "SECOQC White Paper on Quantum Key Distribution and Cryptography," http://arxiv.org/abs/quant-ph/0701168 (2007).
- B. Qi, C. H. Fung, H. K. Lo, and X. Ma, "Time-Shift Attack in Practical Quantum Cryptosystems," Quant. Info. Comput. 7, 73 (2007).
- X. Ma and H. K. Lo, Centre for Quantum Information and Quantum Control, University of Toronto, 10 King�??s College Road, Toronto, ON, M5S 3G4, Canada, (personal communication, 2008).
- X. Ma, C. H. Fung, and H. K. Lo, "Quantum Key Distribution With Entangled Photon Sources," http://arxiv.org/abs/quant-ph/0703122 (2007).
- J. Hasegawa, M. Hayashi, T. Hiroshima, A. Tanaka, and A. Tomita, "Experimental Decoy State Quantum Key Distribution with Unconditional Security Incorporating Finite Statistics," http://arxiv.org/abs/0705.3081 (2007).
- N. J. Beaudry, T. Moroder, and N. L¨utkenhaus, "Squashing Models for Optical Measurements in Quantum Communication," http://arxiv.org/abs/0804.3082 (2008).
- T. Tsurumaru and K. Tamaki, "Security Proof for QKD Systems with Threshold Detectors," http://arxiv.org/abs/0803.4226 (2008).
- M. Koashi, Y. Adachi, T. Yamamoto, and N. Imoto, "Security of Entanglement-Based Quantum Key Distribution with Practical Detectors," http://arxiv.org/abs/0804.0891 (2008).
- N. Lutkenhaus, Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada, (personal communication, 2008).
- C. H. Bennett, G. Brassard, and N. D. Mermin, "Quantum Cryptography without Bell�??s Theorem," Phys. Rev. Lett. 68, 557 (1992). [CrossRef] [PubMed]
- For more complete details about the system please refer to [22] and [23].
- C. Erven, "On Free Space Quantum Key Distribution and its Implementation with a Polarization-Entangled Parametric Down Conversion Source," Master�??s thesis, University of Waterloo (2007).
- G. Weihs and C. Erven, "Entangled Free-Space Quantum Key Distribution," Proc. SPIE 6780, 1-9 (2007).
- P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337 (1995). [CrossRef] [PubMed]
- NIST, "NIST Timing Software,"http://tf.nist.gov/service/its.htm (2008).
- G. Brassard and L. Salvail, "Secret-Key Reconciliation by Public Discussion," Lect. Notes Comput. Sci. 765, 410 (1994). [CrossRef]
- J. L. Carter and M. N. Wegman, "Universal Classes of Hash Functions," J. Comput. Syst. Sci. 18, 143 (1979). [CrossRef]
- T. Sugimoto and K. Yamazaki, "A Study on Secret Key Reconciliation Protocol "Cascade," IEICE Trans. FundamentalsE 83ANo. 10, 1987 (2000).

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