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.