If you think about it, this is fundamentally not possible. There is no way of authenticating who sits on the other end of your fiber connection without having previously exchanged a key. This could either be a shared secret key, or standard public key cryptography.
From an it-security perspective, QKD is simply a very expensive and impractical stream cipher that (slowly) grows a short shared secret key into an arbitrarily long one. The only fundamental advantage over a symmetric encryption algorithm like AES is that an attack would have to happen during the QKD process when the (signed) basis settings are exchanged. It is not possible to simply record all the communication with the hope to maybe being able to break the algorithm in the far future.