What is the meaning of coherent states of mean photon number

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I am studying Quantum Cryptography and I am quite new in Quantum area. I have read an article and I found this confusing statement:
upload_2018-5-17_17-19-48.png

My questions:
1. The three stage protocol implementing multiphoton. What is the meaning of coherent states of mean photon number?
2. How to describe the quantum state by density matrix?

Hopefully that anyone can help me to clarify on this matter, in layman's term. ;)
Thank you.
 

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