  Random generation and confidential distribution of cryptographic keys are
fundamental building blocks of secure communication. Using quantum states in
which the transmitted quantum bit is entangled with a stationary memory quantum
bit allows the secure generation and distribution of keys to be based on
fundamental properties of quantum mechanics. At the same time, the reach of
secure communication networks can be enhanced, in particular, since this
architecture would be compatible with quantum repeaters which are an integral
part for scaling quantum networks. Here, we realize a true single-photon
quantum key distribution protocol (BBM92 protocol) at a second-order temporal
correlation of $ {g^{(2)}(0)=0.00(5)}$ involving an entangled memory qubit
which enables us to produce a certified random secret key on both endpoints of
the quantum communication channel. We certify the randomness of the key using
the min-entropy of the atom-photon state arising from the violation of the CHSH
version of the Bell inequality of $ 2.33(6)$.
