High-rate and high-capacity measurement-device-independent quantum key distribution with Fibonacci matrix coding in free space

This paper proposes a high-rate and high-capacity measurement-device-independent quantum key distribution (MDI-QKD) protocol with Fibonacci-valued and Lucas-valued orbital angular momentum (OAM) entangled states in free space. In the existing MDI-OAM-QKD protocols, the main encoding algorithm handles encoded numbers in a bit-by-bit manner. To design a fast encoding algorithm, we introduce a Fibonacci matrix coding algorithm, by which, encoded numbers are separated into segments longer than one bit. By doing so, when compared to the existing MDI-OAM-QKD protocols, the new protocol can effectively increase the key rate and the coding capacity. This is because Fibonacci sequences are used in preparing OAM entangled states, reducing the misattribution errors (which slow down the execution cycle of the entire QKD) in QKD protocols. Moreover, our protocol keeps the data blocks as small as possible, so as to have more blocks in a given time interval. Most importantly, our proposed protocol can distill multiple Fibonacci key matrices from the same block of data, thus reducing the statistical fluctuations in the sample and increasing the final QKD rate. Last but not the least, the sender and the receiver can omit classical information exchange and bit flipping in the secure key distillation stage.