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Chinese Physics Letters

Analysis of Faraday Mirror in Auto-Compensating Quantum Key Distribution

Kejin Wei, Haiqiang Ma, Ruixue Li, Wu Zhu, Hongwei Liu, Yong Zhang, Rongzhen Jiao

Published Aug 1, 2015• 1 citation

Abstract

The 'plug & play' quantum key distribution system is the most stable and the earliest commercial system in the quantum communication field. Jones matrix and Jones calculus are widely used in the analysis of this system and the improved version, which is called the auto-compensating quantum key distribution system. Unfortunately, existing analysis has two drawbacks: only the auto-compensating process is analyzed and existing systems do not fully consider laser phase affected by a Faraday mirror (FM). In this work, we present a detailed analysis of the output of light pulse transmitting in a plug & play quantum key distribution system that contains only an FM, by Jones calculus. A similar analysis is made to a home-made auto-compensating system which contains two FMs to compensate for environmental effects. More importantly, we show that theoretical and experimental results are different in the plug & play interferometric setup due to the fact that a conventional Jones matrix of FM neglected an additional phase π on alternative polarization direction. To resolve the above problem, we give a new Jones matrix of an FM according to the coordinate rotation. This new Jones matrix not only resolves the above contradiction in the plug & play interferometric setup, but also is suitable for the previous analyses about auto-compensating quantum key distribution.

DOI: 10.1088/0256-307x/32/8/080303

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The 'plug & play' quantum key distribution system is the most stable and the earliest commercial system in the quantum communication field. Jones matrix and Jones calculus are widely used in the analysis of this system and the improved version, which is called the auto-compensating quantum key distribution system. Unfortunately, existing analysis has two drawbacks: only the auto-compensating process is analyzed and existing systems do not fully consider laser phase affected by a Faraday mirror (FM). In this work, we present a detailed analysis of the output of light pulse transmitting in a plug & play quantum key distribution system that contains only an FM, by Jones calculus. A similar analysis is made to a home-made auto-compensating system which contains two FMs to compensate for environmental effects. More importantly, we show that theoretical and experimental results are different in the plug & play interferometric setup due to the fact that a conventional Jones matrix of FM neglected an additional phase π on alternative polarization direction. To resolve the above problem, we give a new Jones matrix of an FM according to the coordinate rotation. This new Jones matrix not only resolves the above contradiction in the plug & play interferometric setup, but also is suitable for the previous analyses about auto-compensating quantum key distribution.

This report proposes a “Plug and Play” quantum key distribution system using differential phase shift, in which any birefringence effects and polarization-dependent losses in the telecom fiber are automatically compensated by using a Faraday mirror. In this system, a light pulse is split into three pulses after traveling through four couplers and a light intensity feedback servosystem is plugged into this system in order to adjust the phase shifter to compensate the variation of these three pulses. The efficiency of key creation in this system is 8/3 higher than the conventional cryptosystem based on the BB84 protocol.

To compensate for all polarization fluctuations in the transmitting fiber by using Faraday mirror is discussed, and and- system based on Faraday mirror for quantum cryptography is introduced, phase-encoding analysis in brief for plug- and- play system is implemented. The interfering pulses follow exactly the same spatial path, ensuring very high stability and self-compensating. The use of Faraday mirrors compensates for automatically any birefringence effects and polarization dependent losses in the transmitting fiber.

The Faraday mirror (FM) plays a very important role in maintaining the stability of two-way plug-and-play quantum key distribution (QKD) systems. However, the practical FM is imperfect, which will not only introduce an additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper we propose a passive Faraday mirror attack in two-way QKD system based on the imperfection of FM. Our analysis shows that if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish these states with a set of Positive Operator Valued Measure (POVM) operators belonging to three-dimension space, which will reduce the QBER induced by her attack. Furthermore, a relationship between the degree of the imperfection of FM and the transmittance of the practical QKD system is obtained. The results show that the probability that Eve loads her attack successfully depends on the degree of the imperfection of FM rapidly, but the QBER induced by Eve's attack changes slightly with the degree of the FM imperfection.

We propose an auto-compensating differential phase shift scheme for quantum key distribution with a high key-creation efficiency, which skillfully makes use of automatic alignment of the photon polarization states in optical fiber with modified Michelson interferometers composed of unequal arms with Faraday mirrors at the ends. The Faraday-mirrors-based Michelson interferometers not only function as pulse splitters, but also enable inherent compensation of polarization mode dispersion in the optic-fiber paths at both Alice's and Bob's sites. The sequential pulses encoded by differential phase shifts pass through the quantum channel with the same polarization states, resulting in a stable key distribution immune to the polarization mode dispersion in the quantum channel. Such a system features perfect stability and higher key creation efficiency over traditional schemes.

We present a time-multiplexed interferometer based on Faraday mirrors, and apply it to quantum key distribution. The interfering pulses follow exactly the same spatial path, ensuring very high stability and self balancing. Use of Faraday mirrors compensates automatically any birefringence effects and polarization dependent losses in the transmitting fiber. First experimental results show a fringe visibility of 0.9984 for a 23km-long interferometer, based on installed telecom fibers. In so-called private-key cryptographic systems, secure transmission through unprotected channels rely on the exchange of secret keys, known only to the sender, Alice, and the receiver, Bob. Quantum cryptography (QC) relies on the properties of quantum mechanics to obtain a provably secure key distribution [1, 2, 3, 4]. Most exisiting implementations rely on either the polarization [2, 5, 6] or the phase [7, 8, 9, 10] of very weak pulses of light as information carrier. To date, the longest transmission spans were obtained in optical fibers, at a wavelength of 1300 nm [6, 9, 10]. The main difficulty with polarization-based systems is the need to keep stable polarizations over distances of tens of kilometers, in standard telecom cables. Indeed, due to the birefringence of the fibers and the effect of the environment, the output polarization fluctuates randomly. Recent experiments [6]