Security bound of continuous-variable quantum key distribution with noisy coherent states and channel

Security of a continuous-variable quantum key distribution protocol based on noisy coherent states and channel is analyzed. Assuming the noise of coherent states is induced by Fred, a neutral party relative to others, we prove that the prepare and measurement scheme and entanglement-based scheme are equivalent. Then, we show that this protocol is secure against Gaussian collective attacks even if the channel is lossy and noisy, and further, a lower bound to the secure key rate is derived.