内容：

Coherent state photon sources are widely used in quantum information processing. In many applications, a coherent state is functioned as a mixture of Fock states by assuming its phase is continuously randomized. In practice, such a crucial assumption is often not satisfied and, therefore, the security of the protocol is not guaranteed. To bridge this gap, we show that a discrete phase randomized source can well approximate its continuous counterpart. As an application, we give security bounds for discrete phase quantum key distribution schemes, which can be easily realized in practice and our simulation shows that with only a small number (say, 10) of discrete phases, the performance of discrete phase randomization is very close to the continuous one. Comparing to the conventional continuous phase randomization case, where an infinite amount of random bits are required, our result shows that only a small amount (say, 4 bits) of randomness is needed.

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