Security of quantum key distribution protocols using two-way classical communication or weak coherent pulses

A fundamental problem in cryptography is to enable two distant parties, traditionally called Alice and Bob, to communicate in absolute privacy, even in presence of an eavesdropper, Eve. It is a well known fact that a secret key, i.e., a randomly chosen bit string held by both Alice and Bob, but unknown to Eve, is sufficient to perform this task (one-time pad encryption). Thus, the problem of secret communication reduces to the problem of distributing a secret key.