On the Poisson approximation to photon distribution for faint lasers

The photon number statistics for attenuated faint laser pulses is quantitatively studied. It confirms that, even for a non-Poissonian laser source, after being attenuated into faint laser with ultra-low mean photon number, the photon number distribution would approximately be a Poisson distribution. The error of such an approximation is estimated, and numerical tests verify our theoretical analysis. This work lays a sound mathematical foundation for the well-known intuitive idea which has been widely used in quantum cryptography.