The public key is shared, however, the private key is always kept secret for decrypting purpose. And in that manner public and private transaction takes place. However, the quantum cryptography is different, as it does the task which are supposed to be almost impossible with the help of traditional cryptography. It make use of the subtle features of the quantum mechanics like the no-cloning theoren or the Heisenberg principle of uncertainty. And that is why it is different from public and private key sort of thinking.
