Characterizing photon-number distribution of pulsed sources using non–photon-number-resolving detectors for quantum key distribution

Quantum key distribution (QKD) has a prospect to realize unconditional secure communication. However, many real system problems should be solved. Transmitters security is an important part of QKD security. And measuring photon number distribution could help improve it. This measurement is also useful for measuring unknown sources or testing newly designed sources. In this article, a method to measure the photon number distribution of pulses using non-photon-number-resolving detectors is proposed. Numerical simulation is conducted to test this scheme and performs well. Experiment on Poisson source is also used to test this method.

Figure 1

Our scheme model. $P{I}_i$'s are the probabilities that a photon goes into each SPAD.

Figure 2

The simulation results and theoretical distribution. Mean photon numbers of (a)–(d) are 0.2, 0.3, 0.5, and 0.7.

Figure 3

Our experimental setup. Devices are described in the text.

Figure 4

The experimental results and theoretical distribution. Mean photon numbers of (a)–(e) are 0.146, 0.253, 0.405, 0.513, and 0.638.

Figure 5

The measurement results and theoretical results when the mean photon number is 0.916. Here the $X$-axis values from 0 to 15 represent response (0000, 1000, 0100, 0010, 0001, 1100, 1010, 1001, 0110, 0101, 0011, 1110, 1101, 1011, 0111, 1111) separately.