New protocols for non-orthogonal quantum key distribution

Combining passive decoy-state idea with active decoy-state idea, a non-orthogonal (SARG04) decoy-state protocol with one vacuum and two weak decoy states is introduced based on a heralded pair coherent state photon source for quantum key distribution. Two special cases of this protocol are deduced, i.e., one-vacuum-and-one-weak-decoy-state protocol and one-weak-decoy-state protocol. In these protocols, the sender prepares decoy states actively, which avoids the crude estimation of parameters in SARG04 passive decoy-state method. With passive decoy-state idea, the detection events on Bob's side that are non-triggered on Alice's side are not discarded, but used to estimate the fractions of single-photon and two-photon pulses, which offsets the limitation of the detector's low efficiency and overcomes the shortcoming that the performance of active decoy-state protocol severely depends on detector's efficiency of sender. The simulation results show that the combination of active and passive decoy-state idea increases the key generation rate. With one-vacuum-and-two-weak-decoy-state protocol, one can achieve a key generation rate that is close to the theoretical limit of an infinite decoy-state protocol. The performance of the other two protocols is a little less than with the former, but the implementation is easier. Under the same condition of implementation, higher key rates can be obtained with our protocols than with existing methods.