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Optics Express

High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing

Zhen Qu, Ivan B. Djordjević

Published Mar 28, 2017• 70 citations
Publisher

Abstract

A high-speed four-state continuous-variable quantum key distribution (CV-QKD) system, enabled by wavelength-division multiplexing, polarization multiplexing, and orbital angular momentum (OAM) multiplexing, is studied in the presence of atmospheric turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns yielding Andrews' spectrum are recorded. The phase noise is mitigated by the phase noise cancellation (PNC) stage, and channel transmittance can be monitored directly by the D.C. level in our PNC stage. After the system calibration, a total SKR of >1.68 Gbit/s can be reached in the ideal system, featured with lossless channel and free of excess noise. In our experiment, based on commercial photodetectors, the minimum transmittances of 0.21 and 0.29 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission, while a total SKR of 120 Mbit/s can be obtained in case of mean transmittances.

DOI
10.1364/oe.25.007919

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A high-speed four-state continuous-variable quantum key distribution (CV-QKD) system, enabled by wavelength-division multiplexing, polarization multiplexing, and orbital angular momentum (OAM) multiplexing, is studied in the presence of atmospheric turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns yielding Andrews' spectrum are recorded. The phase noise is mitigated by the phase noise cancellation (PNC) stage, and channel transmittance can be monitored directly by the D.C. level in our PNC stage. After the system calibration, a total SKR of >1.68 Gbit/s can be reached in the ideal system, featured with lossless channel and free of excess noise. In our experiment, based on commercial photodetectors, the minimum transmittances of 0.21 and 0.29 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission, while a total SKR of 120 Mbit/s can be obtained in case of mean transmittances.
We experimentally demonstrate an eight-state continuous-variable quantum key distribution (CV-QKD) over atmospheric turbulence channels. The high secret key rate (SKR) is enabled by 4-D multiplexing of 96 channels, i.e., six-channel wavelength-division multiplexing, four-channel orbital angular momentum multiplexing, two-channel polarization multiplexing, and two-channel spatial-position multiplexing. The atmospheric turbulence channel is emulated by a spatial light modulator on which a series of azimuthal phase patterns yielding Andrews' spectrum are recorded. A commercial coherent receiver is implemented at Bob's side, followed by a phase noise cancellation stage, where channel transmittance can be monitored accurately and phase noise can be effectively eliminated. Compared to four-state CV-QKD, eight-state CV-QKD protocol potentially provides a better performance by offering higher SKR, better excess noise tolerance, and longer secure transmission distance. In our proposed CV-QKD system, the minimum transmittances of 0.24 and 0.26 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission. A maximum SKR of 3.744 Gb/s is experimentally achievable, while a total SKR of 960 Mb/s can be obtained in case of mean channel transmittances.
In this invited paper, a high-speed continuous-variable quantum key distribution (CV-QKD) system is investigated in the presence of atmospheric turbulence, which is enabled by employing the wavelength, polarization, and orbital angular momentum (OAM) states as degrees of freedom. Four-state discrete modulation is used for the key shaping for the convenience of easy generation, as well as to enhance the reconciliation efficiency. The polarization insensitive atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which randomly generated azimuthal phase patterns yielding Andrews' spectrum are recorded. The phase noise is mitigated by the phase noise cancellation (PNC) stage, and transmittance fluctuation is monitored directly by the D.C. component in the PNC stage. After system calibration, a total secret key rate (SKR) of 240 Mb/s can be reached in the presence of atmospheric turbulence.
We experimentally demonstrate a RF-assisted four-state continuous-variable quantum key distribution (CV-QKD) system in the presence of turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns are recorded yielding Andrews’ azimuthal phase spectrum. Frequency and phase locking are not required in our system thanks to the proposed digital phase noise cancellation (PNC) stage. Besides, the transmittance fluctuation can be monitored accurately by the DC level in this PNC stage, which is free of post-processing noise. The mean excess noise is measured to be 0.014, and the maximum secret key rate of >20Mbit/s can be obtained with the transmittance of 0.85, while employing the commercial PIN photodetectors.
We propose and experimentally investigate a high-speed Kramers-Kronig (KK) scheme based continuous-variable quantum key distribution (CV-QKD) system over a free-space optical (FSO) channel. The atmospheric turbulence channel is emulated by three spatial light modulators on which three randomly generated azimuthal phase patterns yielding Andrews' spectrum are recorded. The proposed KK scheme enables a low-complexity implementation, insensitivity to laser phase noise, low detection noise, and accurate channel transmittance monitoring. In addition, eight state CV-QKD protocols and 10-channels wavelength-division multiplexing (WDM) scheme are experimentally verified to obtain a high secure key rate. In our experiment, the minimum transmittance of 0.6 is required to guarantee the secure transmission, and a total SKR of 2.1 Gb/s can be obtained at the mean transmittance in weak turbulence regime.
In principle, the number of orbital angular momentum (OAM) eigenstates is unbounded; therefore, OAM multiplexing could greatly increase the transmission rate. Compared with optical fibers, free-space channels fluctuate randomly over time due to the effects of atmospheric turbulence. Free-space channel estimation is necessary. Here, we study the channel parameter estimation of continuous-variable quantum key distribution (CVQKD) based on OAM, especially the influence of atmospheric turbulence on transmittance and excess noise. By comparing the secret key rate in the case of single link and multiplexing, the impact of the estimated parameters on the performance of the CVQKD system is evaluated. Simulation results show that the value of the estimated parameter will affect the secret key rate.
Quantum secure direct communication (QSDC) with the feature of allowing secret messages to be communicated directly over quantum channels has two approaches including discrete variable and continuous variable (CV). Among of them, the CVQSDC system indicates the advantages of high secrecy capacity and low experimental cost. As the number of eigenstates is unbounded, the orbital angular momentum (OAM) is an efficient method to increase the secrecy capacity in a CVQSDC system. However, OAM is very vulnerable to atmospheric turbulence, resulting in a phase distortion quantum state. In this work, we propose a CVQSDC protocol with OAM multiplexing, and reveal how the channel parameters, especially transmittance and excess noise, are influenced by atmospheric effects through the simulation experiment. On this basis, the security of the system is further analyzed and the secrecy capacity calculated. The results indicated that the increase in turbulence intensity leads to enhanced crosstalk between the OAM angular modes, which in turn leads to a decrease in the effective transmittance and an increase in the excess noise. Meanwhile, the results also showed that the secrecy capacity decreases with the increase of transmission distance, atmospheric turbulence intensity, and angular mode; in addition, OAM multiplexing can obtain more secrecy capacity compared with a single link.