## Four–photon interferometry for secure quantum key distribution

Optics Express, Vol. 10, Issue 21, pp. 1222-1226 (2002)

http://dx.doi.org/10.1364/OE.10.001222

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### Abstract

We introduce a quantum key distribution scheme based on four-photon coincidence measurements. This scheme offers a much higher degree of security than current quantum key distribution methods and minimizes problems due to photon losses and dark counts.

© 2002 Optical Society of America

*ϕ*+

_{A}*θ*) and (

*ϕ*+

_{B}*θ*), with

*θ*=

*ω*Δ

_{p}*T*= 2

*mπ*, where

*m*is an integer, the coefficient of correlation of the four outputs is [4

4. A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. **69**, 1293–1295 (1992). [CrossRef] [PubMed]

8. H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. **85**, 3313–3316 (2000). [CrossRef] [PubMed]

9. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, “Polarization state of a biphoton:Quantum ternary logic,” Phys. Rev. A **60**, R4209–R4212 (1999). [CrossRef]

11. T. B. Pittman, “On the Use of Double Entanglement in Four-Photon Experiments,” Phys. Lett. A **204**, 193–197 (1995). [CrossRef]

12. D. Bouwmeester, J. -W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement,” Phys. Rev. Lett. **82**, 1345–1349 (1999). [CrossRef]

13. J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation,” Phys. Rev. Lett. **86**, 4435–4438 (2001). [CrossRef] [PubMed]

14. Z. Zhao, J. -W. Pan, and M. S. Zhan, “Practical Scheme for Entanglement Concentration,” Phys. Rev. A **64**014301 (2001). [CrossRef]

15. H. Weinfurter and M. Zukowski, “Four-Photon Entanglement From Down-Conversion,” Phys. Rev. A **64**, 010102(R) (2001). [CrossRef]

16. F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, “Four Qubits Can Be Entangled in Nine Different Ways,” Phys. Rev. A **65**, 052112 (2002). [CrossRef]

13. J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation,” Phys. Rev. Lett. **86**, 4435–4438 (2001). [CrossRef] [PubMed]

17. S. P. Tewari and P. Hariharan, “Generation of entangled 4-photon states by parametric downconversion,” J. Mod. Opt. **44**, 543–553 (1997). [CrossRef]

18. P. Hariharan, J. Samuel, and S. Sinha “Four-photon interference: a realizable experiment to demonstrate violation of EPR postulates for perfect correlations,” J. Opt. B: Quantum Semiclass. **1**, 199–205 (1999). [CrossRef]

*μ*s, at a repetition rate of 10 pulses s

^{-1}, it should be possible to obtain a peak power that is 10

^{5}greater than the average power and an improvement in down-conversion efficiency by a factor of this order.

20. M. Oberparleiter and H. Weinfurter, “Cavity-enhanced generation of polarization-entangled photon pairs,” Opt. Commun. **183**, 133–137 (2000). [CrossRef]

^{-1}.

18. P. Hariharan, J. Samuel, and S. Sinha “Four-photon interference: a realizable experiment to demonstrate violation of EPR postulates for perfect correlations,” J. Opt. B: Quantum Semiclass. **1**, 199–205 (1999). [CrossRef]

*T*greater than the coherence time of the down–converted photons, so that no interference effects due to single photons are observed in the individual interferometers.

_{1}, D

_{2}, D

_{3}and D

_{4}is

*ϕ*and Δ

_{A}*ϕ*, chosen at random to have values of 0 or

_{B}*π*, and record coincidences in the outputs from their pairs of interferometers. After a sufficiently large number of coincidences have been recorded, A and B discard all measurements in which either or both of them failed to detect coincidences and convert the results of their measurements into a binary key using a table similar to Table 1.

*ϕ*and Δ

_{A}*ϕ*; however, no information on these phase shifts is exchanged between A and B.

_{B}*ϕ*or Δ

_{A}*ϕ*and the probability of a coincidence in the outputs from the four interferometers, or from either pair of interferometers. In addition, the counts at the outputs from the individual interferometers do not depend on the phase shifts introduced in them. As a result, even if E has control of the source, she cannot obtain any information on the key from an intercept-resend attack.

_{B}21. P. Hariharan, “Simple, high-efficiency, single-photon trap detectors,” J. Opt. B: Quantum Semiclass. **1**, 522–523 (1999). [CrossRef]

^{-1}. This key could be stored and used to encrypt data which could then be transmitted over an open channel at much higher rates.

^{-1}, and since these dark counts occur at random, the probability of detecting a four-fold coincidence in a time window of 1.5 ns (the time resolution of a fast photodetector) is negligible.

## References and links

1. | C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” in |

2. | C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. |

3. | W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. |

4. | A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. |

5. | J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. |

6. | G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on Practical Quantum Cryptography,” Phys. Rev. Lett. |

7. | S. J. D. Phoenix, S. M. Barnett, and A. Chefles, “Three-state quantum cryptography,” J. Mod. Opt. |

8. | H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. |

9. | A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, “Polarization state of a biphoton:Quantum ternary logic,” Phys. Rev. A |

10. | Y. H. Shih and M. H. Rubin, “Four-Photon Interference Experiment for the Testing of the Greenberger-Horne-Zeilinger Theorem,” Phys. Lett. A |

11. | T. B. Pittman, “On the Use of Double Entanglement in Four-Photon Experiments,” Phys. Lett. A |

12. | D. Bouwmeester, J. -W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement,” Phys. Rev. Lett. |

13. | J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation,” Phys. Rev. Lett. |

14. | Z. Zhao, J. -W. Pan, and M. S. Zhan, “Practical Scheme for Entanglement Concentration,” Phys. Rev. A |

15. | H. Weinfurter and M. Zukowski, “Four-Photon Entanglement From Down-Conversion,” Phys. Rev. A |

16. | F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, “Four Qubits Can Be Entangled in Nine Different Ways,” Phys. Rev. A |

17. | S. P. Tewari and P. Hariharan, “Generation of entangled 4-photon states by parametric downconversion,” J. Mod. Opt. |

18. | P. Hariharan, J. Samuel, and S. Sinha “Four-photon interference: a realizable experiment to demonstrate violation of EPR postulates for perfect correlations,” J. Opt. B: Quantum Semiclass. |

19. | P. Hariharan and B. C. Sanders, “Cavity-enhanced parametric down-conversion as a source of correlated photons,” J. Mod. Opt. |

20. | M. Oberparleiter and H. Weinfurter, “Cavity-enhanced generation of polarization-entangled photon pairs,” Opt. Commun. |

21. | P. Hariharan, “Simple, high-efficiency, single-photon trap detectors,” J. Opt. B: Quantum Semiclass. |

**OCIS Codes**

(270.4180) Quantum optics : Multiphoton processes

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Research Papers

**History**

Original Manuscript: August 15, 2002

Revised Manuscript: October 16, 2002

Published: October 21, 2002

**Citation**

P. Hariharan and Barry Sanders, "Four-photon interferometry for secure quantum key distribution," Opt. Express **10**, 1222-1226 (2002)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-21-1222

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### References

- C. H. Bennett and G. Brassard, �??Quantum Cryptography: Public Key Distribution and Coin Tossing,�?? in Proc. of IEEE Inter. Conf. on Computers, Systems and Signal Processing, Bangalore, India (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 175�??179.
- C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, �??Experimental quantum cryptography,�?? J. Cryptol. 5, 3�??28 (1992). [CrossRef]
- W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, �??Quantum cryptography using entangled photons in energy�??time Bell states,�?? Phys. Rev. Lett. 84, 4737 (2000). [CrossRef] [PubMed]
- A. K. Ekert, J. G. Rarity, P. R. Tapster and G. M. Palma, �??Practical quantum cryptography based on two�??photon interferometry,�?? Phys. Rev. Lett. 69, 1293�??1295 (1992). [CrossRef] [PubMed]
- J. D. Franson, �??Bell inequality for position and time,�?? Phys. Rev. Lett. 62, 2205�??2208 (1989). [CrossRef] [PubMed]
- G. Brassard, N. Lutkenhaus, T. Mor and B. C. Sanders, �??Limitations on Practical Quantum Cryptography,�?? Phys. Rev. Lett. 85, 1330�??1333 (2000). [CrossRef] [PubMed]
- S. J. D. Phoenix, S. M. Barnett and A. Chefles, �??Three-state quantum cryptography,�?? J. Mod. Opt. 47, 507�??516 (2000).
- H. Bechmann�??Pasquinucci and A. Peres, �??Quantum cryptography with 3�??state systems,�?? Phys. Rev. Lett. 85, 3313�??3316 (2000). [CrossRef] [PubMed]
- A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, �??Polarization state of a biphoton:Quantum ternary logic,�?? Phys. Rev. A 60, R4209�??R4212 (1999). [CrossRef]
- Y. H. Shih and M. H. Rubin, �??Four-Photon Interference Experiment for the Testing of the Greenberger-Horne-Zeilinger Theorem,�?? Phys. Lett. A 204, 16�??22 (1995).
- T. B. Pittman, �??On the Use of Double Entanglement in Four-Photon Experiments,�?? Phys. Lett. A 204, 193�??197 (1995). [CrossRef]
- D. Bouwmeester, J. -W. Pan, M. Daniell, H. Weinfurter and A. Zeilinger, �??Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement,�?? Phys. Rev. Lett. 82, 1345�??1349 (1999). [CrossRef]
- J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs and A. Zeilinger, �??Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation,�?? Phys. Rev. Lett. 86, 4435�??4438 (2001). [CrossRef] [PubMed]
- Z. Zhao, J. -W. Pan, and M. S. Zhan, �??Practical Scheme for Entanglement Concentration,�?? Phys. Rev. A 64 014301 (2001). [CrossRef]
- H. Weinfurter and M. Zukowski, �??Four-Photon Entanglement From Down-Conversion,�?? Phys. Rev. A 64, 010102(R) (2001). [CrossRef]
- F. Verstraete, J. Dehaene, B. De Moor and H. Verschelde, �??Four Qubits Can Be Entangled in Nine Di.erent Ways,�?? Phys. Rev. A 65, 052112 (2002). [CrossRef]
- S. P. Tewari and P. Hariharan, �??Generation of entangled 4-photon states by parametric downconversion,�?? J. Mod. Opt. 44, 543�??553 (1997). [CrossRef]
- P. Hariharan, J. Samuel and S. Sinha �??Four-photon interference: a realizable experiment to demonstrate violation of EPR postulates for perfect correlations,�?? J. Opt. B: Quantum Semiclass. 1, 199�??205 (1999). [CrossRef]
- P. Hariharan and B. C. Sanders, �??Cavity-enhanced parametric down-conversion as a source of correlated photons,�?? J. Mod. Opt. 47, 1739�??1744 (2000).
- M. Oberparleiter and H. Weinfurter, �??Cavity-enhanced generation of polarization-entangled photon pairs,�?? Opt. Commun. 183, 133�??137 (2000). [CrossRef]
- P. Hariharan, �??Simple, high-efficiency, single-photon trap detectors,�?? J. Opt. B: Quantum Semiclass. 1, 522�??523 (1999). [CrossRef]

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