Abstract: The study briefly introduces the historical development along with some raising concerns of quantum computing and proposes some quantum applications in solving cryptography problems. Quantum cryptography is the study of information security based on the laws of quantum physics. Unlike classical cryptography focusing on mathematical complexity of algorithm in protecting information from attacks, quantum cryptography concentrates on the fundamental physical properties of the objects carrying information. These objects are identified by their quantum states which are unattackable by the computational power and will be widely applied in the future. This research paper also presents some main research areas of quantum cryptography and the study of BB84 protocol. In this protocol, a series of polarized photons is used to transmit information on the quantum channel and their states are exchanged via public communication channel.