  Quantum Cryptography or Quantum key distribution (QKD) is a technique that
allows the secure distribution of a bit string, used as key in cryptographic
protocols. When it was noted that quantum computers could break public key
cryptosystems based on number theory extensive studies have been undertaken on
QKD. Based on quantum mechanics, QKD offers unconditionally secure
communication. Now, the progress of research in this field allows the
anticipation of QKD to be available outside of laboratories within the next few
years. Efforts are made to improve the performance and reliability of the
implemented technologies. But several challenges remain despite this big
progress. The task of how to test the apparatuses of QKD For example did not
yet receive enough attention. These devises become complex and demand a big
verification effort. In this paper we are interested in an approach based on
the technique of probabilistic model checking for studying quantum information.
Precisely, we use the PRISM tool to analyze the security of BB84 protocol and
we are focused on the specific security property of eavesdropping detection. We
show that this property is affected by the parameters of quantum channel and
the power of eavesdropper.
