Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel
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TOMS, MOLECULES, OPTICS
Controlled Quantum Key Distribution with ThreePhoton PolarizationEntangled States via the Collective Noise Channel1 Li Donga,b, XiaoMing Xiua,b, YaJun Gaob, and X. X. Yia a
School of Physics and Optoelectronic Technology, Dalian University of Technology Dalian 116024, P. R. China b Department of Physics, College of Mathematics and Physics, Bohai University Jinzhou 121013, P. R. China email: [email protected], [email protected] Received January 27, 2011
Abstract—Using threephoton polarizationentangled GHZ states or W states, we propose controlled quan tum key distribution protocols for circumventing two main types of collective noise, collective dephasing noise, or collective rotation noise. Irrespective of the number of controllers, a threephoton state can generate a onebit secret key. The storage technique of quantum states is dispensable for the controller and the receiver, and it therefore allows performing the process in a more convenient mode. If the photon cost in a security check is disregarded, then the efficiency theoretically approaches unity. DOI: 10.1134/S1063776111130140 1
1. INTRODUCTION
The two recent decades have witnessed rapid devel opment in the theory and practice of quantum com munication. As a relatively mature technique, quan tum key distribution (QKD) enables two legitimate users to establish a shared secret string of bits as a key for encrypting and decrypting secret information. In 1984, Bennett and Brassard put forward the pioneer ing fourstate QKD protocol, BB84 [1], which is the first unconditionally secure key distribution protocol. Decreasing the practical complexity and halving the idealized maximum efficiency of BB84, Bennett pre sented a protocol with two nonorthogonal states in 1992, B92 [2]. Both these protocols are based on sin gleparticle states. In 1991, Ekert proposed a QKD protocol based on Einstein–Podolsky–Rosen (EPR) pairs, E91 [3]. In 1992, by simplifying the complicated Bell inequality to two sets of nonorthogonal bases in the security check, Bennett et al. modified the E91 protocol to BBM92 [4]. Since then, QKD has attracted extensive attention of the researchers and progressed quickly [5–16]. Currently, photons are promising candidates for carriers of quantum information because they are cheap, fast, and interact weakly with the environment. But in actual applications, the polarization of photons is prone to be influenced by thermal and mechanical fluctuations and the imperfections of a quantum channel (e.g., the inhomogeneity of the atmosphere in free space, the birefringence in an optical fiber, mis alignment of the reference frame, and backward emis sion [17]), which can be generally regarded as channel noise. 1
The article is published in the original.
When the noise between the information carriers and the environment is sufficiently weak, the error arises with a low probability. Using a quantum error correction code, the participants utilize several physi cal bits as one logical bit according to the special no
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