Single-photon characteristics of superposed weak coherent states

We study a superposed weak coherent state that can fundamentally mimic an ideal single photon not only with respect to the number of photons but also in terms of an indeterminate phase. It is close to the single-photon state with high fidelity and exhibits fundamental features of single photons such as antibunching and Hong-Ou-Mandel interference. The emergence and vanishing of single-photon characteristics can be directly observed by changing two parameters, i.e., the mean photon number and number of phases. Our result shows that the uncertainty between the photon number and phase indeed constitutes the characteristics of single photons. Finally, we apply the superposed weak coherent state to quantum key distribution and demonstrate that it outperforms the typical approach using phase-randomized weak coherent states.