Causes of bit error and error correction for quantum key distribution protocols

Quantum key distribution protocols (QKD) identify eavesdroppers on quantum channel based on laws of quantum mechanics. In the original BB84 protocol, unauthorized measurements on qubits are discovered after Alice and Bob sacrifice some random resulting key bits as a test and find out a mismatch rate. Decoy state protocol alerts photon number splitting attack when the decoy multiphoton pulses deliberately positioned by Alice are registered abnormally higher at Bob's detectors than the single photon pulses are. E91 protocol is the first QKD protocol that ever brought about entangled atoms. Based on Bell's theorem, a probability coefficient is constrained within a fixed range under the circumstances of interception. While in practice, bit error rate (BER) is not necessarily associated with vicious eavesdropping. Detection inefficiency, transmission loss, imperfect entanglement sources and many other factors contribute as false alarms. Error correction is an essential post-processing procedure to tolerate implementation limits, yet secure the accuracy of the transmitted key. Quantifying third party contaminations also helps setting an optimal BER threshold to decide if one should abandon all previous communications. In this work, we summarize major causes of bit error in various practical QKD protocols mentioned above and study whether error correction models, such as low-density parity-check code (LDPC), perform accordingly to different kinds of errors.