Compton Scattering of Annihilation Photons as a Short Range Quantum Key Distribution Mechanism

Authors: Roman Novak, Matjaz Vencelj

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083871

References:

[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.