Quantum key distribution with a control key

Quantum key distribution (QKD) relies on randomness to exchange secret keys among the communicating parties. While ensuring the secrecy of the keys being distributed, independent randomness also causes to reduce the number of key bits that can be shared per quantum signal exchanged. Recently it was shown that it is possible to use pseudo-randomness in place of true randomness in the QKD without compromising the integrity of a QKD scheme. By the virtue of a short secret key - called a control key - shared among the key sharing parties, same pseudo-randomness can be generated at the transmitter and the receiver end that allow to obtain a higher key exchange rate. However, there are certain modifications which are necessary before pseudo-randomness can be safely employed in a QKD procedure. In this paper, we provide a modification of QKD schemes for a secure use with the control key. We modify the prepare-and-measure (BB84) type, and measurement-device independent protocols. We then verify the advantages of use of control key in terms of key rates for the modification of two QKD schemes.