One Step Quantum Key Distribution Based on EPR Entanglement

www.nature.com/scientificreports OPEN One Step Quantum Key Distribution Based on EPR Entanglement Jian Li1,2, Na Li1,3, Lei-Lei Li1 & Tao Wang1 received: 21 December 2015 accepted: 08 June 2016 Published: 30 June 2016 A novel quantum key distribution protocol is presented, based on entanglement and dense coding and allowing asymptotically secure key distribution. Considering the storage time limit of quantum bits, a grouping quantum key distribution protocol is proposed, which overcomes the vulnerability of first protocol and improves the maneuverability. Moreover, a security analysis is given and a simple type of eavesdropper’s attack would introduce at least an error rate of 46.875%. Compared with the “Pingpong” protocol involving two steps, the proposed protocol does not need to store the qubit and only involves one step. The task of cryptograph is to ensure that only the legitimate users like Alice and Bob can read the secret message in the secure communication, which the unauthorized users like Eve cannot read. Researchers are dedicated to developing reliable and secure cryptographic protocols. With the rapid development of information technology and quantum physics1, quantum cryptography has become an important and attractive field. Quantum cryptography is based on the quantum mechanics, which is definitely different from the classical digital cryptographic system, and has much higher performance of security. With the rapid development of quantum mechanics in the past years, quantum information has been prosperous and fascinating. Quantum mechanics offers some unique capabilities for the processing of the information, such as quantum computation and quantum communication. In the last decade, scientists have made dramatic progress in the field of quantum communication. The quantum key distribution (QKD), which task is to create a private key between two remote authorized users, is one of the most remarkable applications of quantum mechanics. Importantly, Gottesman, Lo, Lütkenhaus and Preskill (henceforth referred to as GLLP) proved the security of QKD when Alice’s and Bob’s devices are flawed, as is the case in practical implementations2. In addition, a device-independent QKD (DI-QKD) and measurement-device-independent QKD (MDI-QKD) was proposed. MDI-QKD protocol is fully practicable with current technology and attracted a lot of scientific attention from theoretical side3–7. In 1984, C. H. Bennett and G. Brassard presented the pioneer quantum key distribution protocol, called BB84 protocol now8. This protocol has received lots of attention since it was come up. IBM and Montreal university first completed the experiment of quantum cryptography in 19899, which verified the BB84 protocol from the aspect of experiment. In ref. 10, the communication distance extended to more than 1 km by use of polarized photons. Now the distance of key distribution can reach up to 200 km, and there are some other developments with quantum key distribution, such as refs 11–16. In recent years, a novel concept, quantum secure direct communication (QSDC) was put forward and studied by groups of researchers. It allows two remote parties to communicate directly without creating a private key in advance and using it to encrypt the secret message. Thus, the sender should confirm whether the channel is secure before he encodes his message on the quantum states because the message cannot be discarded, unlike that in QKD protocols. Many QSDC protocols have been proposed, including the protocols without using entanglement17–19, the protocols using entanglement20–27 and the two-way QSDC protocols28–37. The QSDC protocol can also be used in some special environments as first proposed by Boström et al.38 and Deng et al.20. In ref. 38, Boström and Felbinger presented a famous QSDC protocol which is called “Ping-pong” protocol. But researchers have found much vulnerability39–42 in the “Ping-pong” protocol. A new quantum key distribution protocol was proposed in this paper, which based on entanglement and dense coding. However, in the new protocol, there is a serious problem that is the storage time limit during the actual operation. At present, the world record of quantum state storage time is only 3 ms at Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics. Considering the storage time limit, a grouping quantum key distribution protocol based on entanglement and dense coding, which does 1 School of Computer Science, Beijing University of Posts and Telecommunications, Beijing 100876, China. 2Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China. 3JiLin Medical University, Jilin, 132013, China. Correspondence and requests for materials should be addressed to N.L. (email: ) Scientific Reports | 6:28767 | DOI: 10.1038/srep28767 1 www.nature.com/scientificreports/ Number of classical bits 0 1 2 3 4 5 6 7 8 Classical bits that Alice prepares 1 1 0 0 0 1 1 0 1 0 EPR that Alice prepares Ψ− 06 + Ψ 13 Φ− 25 + Ψ 13 Φ+ 49 Φ− 25 Ψ− 06 Φ− 78 Φ− 78 Φ+ 49 Measurement results that Bob makes Ψ− 06 + Ψ 13 Φ− 25 + Ψ 13 Φ+ 49 Φ− 25 Ψ− 06 Φ− 78 Φ− 78 Φ+ 49 Detection particles Ψ− 06 Φ− 25 Ψ− 06 0 0 1 0 0 1 Φ− 25 Raw key that Bob obtains 1 0 Correction and privacy amplification 1 0 Finial key 9 1001 Table 1. The example of EQKD. not need to store quantum states in process, is proposed. What’s more, the securities of these two protocols are analyzed. Results New QKD Protocol. Referring to the BB84 protocol and “Ping-pong” protocol, a new one step quantum key distribution protocol is proposed, which based on entanglement and dense coding. The entanglement mechanism is introduced to improve the security and the dense coding mechanism is introduced to increase the efficiency of transformation. For simplicity, we suppose that the new quantum key distribution protocol based on entanglement and dense coding in this paper is referred to as EQKD. Now let us give an explicit process for EQKD. For easily understanding the process of EQKD, Table 1 shows an example. (1) Alice prepares a large enough number of classical bits N in sequence, and numbers the bits in the order Alice generates them. (2) Alice prepares enough EPR states in sequence based on the order of classical bit N and dense coding mechanism, and forms a series of particles S in order. Meanwhile, Alice remembers the entanglement states and the location information of every EPR states that the numbers of each EPR quantum bit in sequence S. Then Alice transfers the sequence S to Bob by quantum channel. (3) After Bob received the sequence S that Alice sent, Alice tells Bob the location information of every EPR states by classical channel. (4) Bob extracts every EPR states on the basis of location information of every EPR states, and then makes (...truncated)