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Acta Physica Sinica

Theoretical analysis of polarization tracking based on half-wave plate

Jing Ma, Zhang Guang-Yu, Rong Yi-Wen, Tan Li-Ying, (1)哈尔滨工业大学可调谐激光技术国家级重点实验室,哈尔滨 150001; (2)哈尔滨工业大学可调谐激光技术国家级重点实验室,哈尔滨 150001;哈尔滨理工大学应用科学学院,哈尔滨 150080

Published Jan 1, 2006• 5 citations
Publisher

Abstract

The polarization tracking principle is analyzed by using a half-wave plate in satellite quantum key distribution and the polarization “zero” direction can be corrected by rotation of the half-wave plate. The transforms of six photon polarization states in three conjugative bases are given and the quantum key coding principle based on the polarization tracking is analyzed for the BB84 protocol and B92 protocol.

DOI
10.7498/aps.55.24

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The polarization tracking principle is analyzed by using a half-wave plate in satellite quantum key distribution and the polarization “zero” direction can be corrected by rotation of the half-wave plate. The transforms of six photon polarization states in three conjugative bases are given and the quantum key coding principle based on the polarization tracking is analyzed for the BB84 protocol and B92 protocol.
The BB84 and B92 protocols based on polarization coding are usually used in free-space quantum key distribution. Polarization tracking technique is one of the key techniques in the satellite quantum key distribution. Because the photon polarization state will be changed as a result of the satellite movement, both the transmitter and receiver need to have the ability to track the polarization orientation variation to accomplish the quantum cryptography protocols. In this paper, the polarization tracking principles are analyzed based on Faraday effect and the half-wave plate. The transforms of six photon polarization states in three conjugative bases are given and the quantum key coding principles based on the polarization tracking are analyzed for the BB84 and B92 protocols.
In polarization-encoded free-space quantum communications, a transmitter on a satellite and a receiver in a ground station each have a respective polarization zero direction, by which they encode and decode every polarization quantum bit required for a quantum communication protocol. In order to complete the protocol, the ground-based receiver needs to track and compensate for the polarization zero direction of the satellite-based transmitter. Expressions satisfied by amplitudes of the s-polarization component and the p-polarization component are derived based on a two-mirror model, and a condition satisfied by the reflection coefficients of the two mirrors is given. A polarization tracking principle is analyzed for satellite-to-ground quantum communications, and quantum key encoding and decoding principles based on polarization tracking are given. A half-wave-plate-based dynamic polarization-basis compensation scheme is proposed in this paper, and this scheme is proved to be suitable for satellite-to-ground and intersatellite quantum communications.
Quantum key distribution uses polarization coding.When using conventional single-mode fiber as the channel for quantum state transfer,optical fiber has a slight birefringence and cannot maintain the quantum state of polarization.In this case,this paper proposes a method to make polarization compensation for quantum state.Using the polarization compensation method of successive approximation,it is a promising scheme to complete the polarization compensation by rotating the combination of 2 quarter-wave plate and 1 half-wave plate successively.By measuring the values of polarization contrast ratio,it rotates the three wave plates according to the results of the measurement,until the polarization performance of the system finally meets the requirements.Experimental results show that compared with the polarization compensation method of traversal mode,the method of successive approximation can realize polarization compensation more quickly.
Free-Space Quantum Communication(FSQC) based on the BB84(Bennett-Brassard 1984) protocol makes use of two groups of conjugate basis polarized photon as the carriers of information to realize the communication between a satelits and a group station. Polarization would show some problems like the contrast of polarization to be worser and the polarization-basis unmatched when transfering. In order to achieve the BB84 protocol, ground station needed to track and calibrate for the polarization zero direction of the satellite equipments. So the polarization maintaining and polarization-basis calibrating is one of the key technologies of the FSQC system. Firstly, this paper established the mathematical model of polarization in the FSQC system, and then derived the mathematical relation between the contrast of polarization and the phase delay in theory. Some proposals of Optical System designs have been suggested in the paper. Finally the problem of dynamic polarization-basis in the satellite-ground link had been analysed and the dynamic characteristic of the deviation angle of polarization-basis in this paper.
The study of quantum cryptography is one of the great interest. A straightforward and reliable quantum experiment is provided in this paper. A half wave plate in linearly polarized light makes up a simplified polarization rotator. The polarization rotates twice as much as the half wave plate's fast axis' angle with the polarization plane when the half wave plate is rotated. Here, an experiment of message sharing is conducted to demonstrate quantum communication between parties. The unitary transformation is performed step by step using half-wave plates represented by the Mueller matrix. A simulation created using Python programming has been used to test the proposed protocol's implementation. Python was chosen because it can mathematically imitate the quantum state of superposition.