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Communications in Theoretical Physics

Tomographic Approach in Three-Orthogonal-Basis Quantum Key Distribution*

Wen-Ye Liang, Hao Wen, Zhen−Qiang Yin, Hua Chen, Hong-Wei Li, Wei Chen, Zheng‐Fu Han

Published Sep 1, 2015• 4 citations
Publisher

Abstract

Abstract At present, there is an increasing awareness of some three-orthogonal-basis quantum key distribution protocols, such as, the reference-frame-independent (RFI) protocol and the six-state protocol. For secure key rate estimations of these protocols, there are two methods: one is the conventional approach, and another is the tomographic approach. However, a comparison between these two methods has not been given yet. In this work, with the general model of rotation channel, we estimate the key rate using conventional and tomographic methods respectively. Results show that conventional estimation approach in RFI protocol is equivalent to tomographic approach only in the case of that one of three orthogonal bases is always aligned. In other cases, tomographic approach performs much better than the respective conventional approaches of the RFI protocol and the six-state protocol. Furthermore, based on the experimental data, we illustrate the deep connections between tomography and conventional RFI approach representations.

DOI
10.1088/0253-6102/64/3/295

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Abstract At present, there is an increasing awareness of some three-orthogonal-basis quantum key distribution protocols, such as, the reference-frame-independent (RFI) protocol and the six-state protocol. For secure key rate estimations of these protocols, there are two methods: one is the conventional approach, and another is the tomographic approach. However, a comparison between these two methods has not been given yet. In this work, with the general model of rotation channel, we estimate the key rate using conventional and tomographic methods respectively. Results show that conventional estimation approach in RFI protocol is equivalent to tomographic approach only in the case of that one of three orthogonal bases is always aligned. In other cases, tomographic approach performs much better than the respective conventional approaches of the RFI protocol and the six-state protocol. Furthermore, based on the experimental data, we illustrate the deep connections between tomography and conventional RFI approach representations.
Abstract Recently, a novel reference-frame-independent measurement-device-independent quantum key distribution protocol was proposed, which can remove all detector side channels as well as tolerate unknown and slow variance of reference frame without active alignment. In this paper, we propose a new tomographic method to estimate the key rate in that protocol. We estimate the key rate using conventional method and tomographic method respectively and compare the two methods by numerical simulation. The numerical simulation results show that tomographic approach is equivalent to the conventional approach, which can be used as an alternative method.
Compared with the traditional protocols of quantum key distribution (QKD), the reference-frame-independent (RFI)--QKD protocol has been generally proved to be very useful and practical, since its experimental implementation can be simplified without the alignment of a reference frame. In most RFI-QKD systems, the encoding states are always taken to be perfect, which, however, is not practical in realizations. In this paper, we consider the security of RFI QKD with source flaws based on the loss-tolerant method proposed by Tamaki et al. [Phys. Rev. A 90, 052314 (2014)]. As the six-state protocol can be realized with four states, we show that the RFI-QKD protocol can also be performed with only four encoding states instead of six encoding states in its standard version. Furthermore, the numerical simulation results show that the source flaws in the key-generation basis (Z(Z(Z basis) will reduce the key rate but are loss tolerant, while the ones in XXX and YYY bases almost have no effect and the key rate remains almost the same even when they are very large. Hence, our method and results will have important significance in practical experiments, especially in earth-to-satellite or chip-to-chip quantum communications.
In secure communication, reference-frame calibration is critical to ensuring a secure key rate in quantum key distribution (QKD) systems. This process also increases the complexity of the system, which is not conducive to practical use. Although the reference-frame-independent (RFI) QKD protocol can simplify alignment, it requires three bases to prepare six states. Here the authors present instead a three-state RFI QKD protocol, and verify its security using a recently developed proof based on semidefinite programming. A proof-of-principle experiment is conducted to demonstrate the feasibility of the scheme. This work is sure to boost the practical application of the RFI QKD protocol.
Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is immune to both detector side channel attacks and slow drifts of reference frames, and thus possesses a high level of security. In the traditional protocol of RFI-MDI-QKD, each legitimate user, Alice or Bob, has to prepare six encoding states in three orthogonal bases (X,YX, YX,Y, and ZZZ), which are sent to the untrusted third party, Charlie. Then all the successful counting events are utilized for parameter estimations, which suffer from a severe finite-size effect. In this paper, we propose a scheme on RFI-MDI-QKD with fewer states and demonstrate that it can be secured and made useful by utilizing semidefinite programming. Numerical simulation results reveal the equivalence between those groups of different monitoring states from Alice and Bob. In addition, when considering practical experimental conditions and taking finite-size effects into account, our proposal can achieve a better performance than the traditional six-state RFI-MDI scheme, which provides a resource-saving and simpler state-preparation approach for practical implementations without sacrificing key rates.
Reference-frame-independent quantum key distribution (RFI-QKD) has gained widespread attention due to its unique advantage for practical application, as it circumvents the need for active reference-frame alignment within the system. However, in comparison to the standard BB84 protocol, the original six-state RFI protocol requires a greater number of quantum states to be operated by Alice and Bob, which is an aspect that merits optimization. In this work, we propose a four-state RFI protocol and illustrate that Alice and Bob each require only four quantum states to perform channel estimation that remains independent of reference-frame deviation, which can proficiently reduce the system complexity. Furthermore, through numerical simulations taking the finite-key-size effect into consideration, we show that the four-state RFI protocol can achieve a secure key rate and transmission distance on par with those of the original six-state RFI protocol. Finally, an experiment over 200 km is conducted to evaluate the feasibility of our scheme. We believe that our protocol can streamline the implementation of RFI-QKD and thereby contribute to the practical advancement of RFI-QKD.
Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol that eliminates all possible attacks on the detector side and the necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations since more parameters, e.g., yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy states method estimates these yields overpessimistically since it ignores the potential relations between different bases. Through jointly processing parameters of different bases, the performance of RFI-MDI-QKD is greatly improved in terms of the secret key rate and achievable distance when statistical fluctuations are considered (the statistical fluctuation analysis is the first step to the final analysis of the finite key size effect). Our results pave an avenue towards practical RFI-MDI-QKD.