Compton Scattering of Annihilation Photons as a Short Range Quantum Key Distribution Mechanism
The angular distribution of Compton scattering of two
quanta originating in the annihilation of a positron with an electron
is investigated as a quantum key distribution (QKD) mechanism in
the gamma spectral range. The geometry of coincident Compton
scattering is observed on the two sides as a way to obtain partially
correlated readings on the quantum channel. We derive the noise
probability density function of a conceptually equivalent prepare
and measure quantum channel in order to evaluate the limits of the
concept in terms of the device secrecy capacity and estimate it at
roughly 1.9 bits per 1 000 annihilation events. The high error rate
is well above the tolerable error rates of the common reconciliation
protocols; therefore, the proposed key agreement protocol by public
discussion requires key reconciliation using classical error-correcting
codes. We constructed a prototype device based on the readily
available monolithic detectors in the least complex setup.
[1] R. J. Collins et al., "Quantum key distribution system in standard
telecommunications fiber using a short wavelength single photon
source," J. Appl. Phys., vol. 107, no. 7, pp. 073 102-6, April 2010.
[2] T. Schmitt-Manderbach et al., "Experimental demonstration of freespace
decoy-state quantum key distribution over 144 km," Phys. Rev.
Lett., vol. 98, no. 1, pp. 01 504-4, January 2007.
[3] A. Restelli et al., "Improved timing resolution single-photon detectors in
daytime free-space quantum key distribution with 1.25 GHz transmission
rate," IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 5, pp. 1084-
1090, September/October 2010.
[4] A. Tomaello, C. Bonato, V. D. Deppo, G. Naletto, and P. Villoresi, "Link
budget and background noise for satellite quantum key distribution,"
Advances in Space Research, vol. 47, no. 5, pp. 802-810, March 2011.
[5] V. Scarani, H. Pasquinucci, N. J. Cerf, M. Duˇsek, N. L¨utkenhaus, and
M. Peev, "The security of practical quantum key distribution," Rev. Mod.
Phys., vol. 81, no. 3, pp. 1301-1350, July/September 2009.
[6] C. H. Bennet and G. Brassard, "Quantum cryptography: Public key
distribution and coin tossing," in Proc. IEEE Int. Conf. on Computers,
Systems and Signal Processing, Bangalore, India, 1984, pp. 175-179.
[7] O. Klein and Y. Nishina, "U¨ ber die streung von strahlung durch freie
elektronen nach der neuen relativistischen quantendynamik von dirac,"
Zs. f. Phys., vol. 52, pp. 853-864, 1929.
[8] H. S. Snyder, S. Pasternack, and J. Hornbostel, "Angular correlation of
scattered annihilation radiation," Phys. Rev., vol. 73, no. 5, pp. 440-448,
March 1948.
[9] C. H. Bennet, G. Brassard, and J. M. Robert, "Privacy amplification by
public discussion," SIAM J. Computing, vol. 17, no. 2, pp. 210-229,
1988.
[10] Y. Watanabe, "Privacy amplification for quantum key distribution," J.
Phys. A: Math. Theor., vol. 40, no. 3, pp. F99-F104, January 2007.
[11] U. M. Maurer, "Secret key agreement by public discussion from common
information," IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 733-742, May
1993.
[12] G. Brassard and L. Salvail, "Secret-key reconciliation by public discussion,"
in Proc. EUROCRYPT-93, ser. Lecture Notes in Computer
Science, vol. 765, 1993, pp. 411-423.
[13] T. Sugimoto and K. Yamazaki, "A study on secret key reconciliation
protocol Cascade," IEICE Trans. Fundamentals, vol. E83-A, no. 10, pp.
1987-1991, 2000.
[14] J. Fang, Z. L. Jiang, S. M. Yiu, and L. C. K. Hui, "Checking key integrity
efficiently for high-speed quantum key distribution using combinatorial
group testing," Optics Communications, vol. 284, no. 1, pp. 531-535,
January 2011.
[15] S. F'elix, N. Gisin, A. Stefanov, and H. Zbinden, "Faint laser quantum
key distribution: eavesdropping exploiting multiphoton pulses," J. Mod.
Opt., vol. 48, no. 13, pp. 2009-2021, 2001.
[16] D. Xu, Z. He, and F. Zhang, "Detection of gamma ray polarization
using a 3-D position-sensitive CdZnTe detector," IEEE Trans. Nucl. Sci.,
vol. 52, no. 4, pp. 1160-1164, August 2005.
[17] E. Bleuler and H. L. Bradt, "Correlation between the states of polarization
of the two quanta of annihilation radiation," Phys. Rev., vol. 73,
no. 11, p. 1398, June 1948.
[18] R. Sherr and R. H. Miller, "Electron capture in the decay of Na22,"
Phys. Rev., vol. 93, no. 5, pp. 1076-1081, March 1954.
[1] R. J. Collins et al., "Quantum key distribution system in standard
telecommunications fiber using a short wavelength single photon
source," J. Appl. Phys., vol. 107, no. 7, pp. 073 102-6, April 2010.
[2] T. Schmitt-Manderbach et al., "Experimental demonstration of freespace
decoy-state quantum key distribution over 144 km," Phys. Rev.
Lett., vol. 98, no. 1, pp. 01 504-4, January 2007.
[3] A. Restelli et al., "Improved timing resolution single-photon detectors in
daytime free-space quantum key distribution with 1.25 GHz transmission
rate," IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 5, pp. 1084-
1090, September/October 2010.
[4] A. Tomaello, C. Bonato, V. D. Deppo, G. Naletto, and P. Villoresi, "Link
budget and background noise for satellite quantum key distribution,"
Advances in Space Research, vol. 47, no. 5, pp. 802-810, March 2011.
[5] V. Scarani, H. Pasquinucci, N. J. Cerf, M. Duˇsek, N. L¨utkenhaus, and
M. Peev, "The security of practical quantum key distribution," Rev. Mod.
Phys., vol. 81, no. 3, pp. 1301-1350, July/September 2009.
[6] C. H. Bennet and G. Brassard, "Quantum cryptography: Public key
distribution and coin tossing," in Proc. IEEE Int. Conf. on Computers,
Systems and Signal Processing, Bangalore, India, 1984, pp. 175-179.
[7] O. Klein and Y. Nishina, "U¨ ber die streung von strahlung durch freie
elektronen nach der neuen relativistischen quantendynamik von dirac,"
Zs. f. Phys., vol. 52, pp. 853-864, 1929.
[8] H. S. Snyder, S. Pasternack, and J. Hornbostel, "Angular correlation of
scattered annihilation radiation," Phys. Rev., vol. 73, no. 5, pp. 440-448,
March 1948.
[9] C. H. Bennet, G. Brassard, and J. M. Robert, "Privacy amplification by
public discussion," SIAM J. Computing, vol. 17, no. 2, pp. 210-229,
1988.
[10] Y. Watanabe, "Privacy amplification for quantum key distribution," J.
Phys. A: Math. Theor., vol. 40, no. 3, pp. F99-F104, January 2007.
[11] U. M. Maurer, "Secret key agreement by public discussion from common
information," IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 733-742, May
1993.
[12] G. Brassard and L. Salvail, "Secret-key reconciliation by public discussion,"
in Proc. EUROCRYPT-93, ser. Lecture Notes in Computer
Science, vol. 765, 1993, pp. 411-423.
[13] T. Sugimoto and K. Yamazaki, "A study on secret key reconciliation
protocol Cascade," IEICE Trans. Fundamentals, vol. E83-A, no. 10, pp.
1987-1991, 2000.
[14] J. Fang, Z. L. Jiang, S. M. Yiu, and L. C. K. Hui, "Checking key integrity
efficiently for high-speed quantum key distribution using combinatorial
group testing," Optics Communications, vol. 284, no. 1, pp. 531-535,
January 2011.
[15] S. F'elix, N. Gisin, A. Stefanov, and H. Zbinden, "Faint laser quantum
key distribution: eavesdropping exploiting multiphoton pulses," J. Mod.
Opt., vol. 48, no. 13, pp. 2009-2021, 2001.
[16] D. Xu, Z. He, and F. Zhang, "Detection of gamma ray polarization
using a 3-D position-sensitive CdZnTe detector," IEEE Trans. Nucl. Sci.,
vol. 52, no. 4, pp. 1160-1164, August 2005.
[17] E. Bleuler and H. L. Bradt, "Correlation between the states of polarization
of the two quanta of annihilation radiation," Phys. Rev., vol. 73,
no. 11, p. 1398, June 1948.
[18] R. Sherr and R. H. Miller, "Electron capture in the decay of Na22,"
Phys. Rev., vol. 93, no. 5, pp. 1076-1081, March 1954.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63920", author = "Roman Novak and Matjaz Vencelj", title = "Compton Scattering of Annihilation Photons as a Short Range Quantum Key Distribution Mechanism", abstract = "The angular distribution of Compton scattering of two
quanta originating in the annihilation of a positron with an electron
is investigated as a quantum key distribution (QKD) mechanism in
the gamma spectral range. The geometry of coincident Compton
scattering is observed on the two sides as a way to obtain partially
correlated readings on the quantum channel. We derive the noise
probability density function of a conceptually equivalent prepare
and measure quantum channel in order to evaluate the limits of the
concept in terms of the device secrecy capacity and estimate it at
roughly 1.9 bits per 1 000 annihilation events. The high error rate
is well above the tolerable error rates of the common reconciliation
protocols; therefore, the proposed key agreement protocol by public
discussion requires key reconciliation using classical error-correcting
codes. We constructed a prototype device based on the readily
available monolithic detectors in the least complex setup.", keywords = "Compton scattering, gamma-ray polarization, quantumcryptography, quantum key distribution", volume = "5", number = "7", pages = "1087-7", }