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Chinese Physics Letters

Decoy State Quantum Key Distribution via Beam-Wandering Modeled Atmosphere Channel

ShengLi Zhang, Chenhui Jin, Jiansheng Guo, Jianhong Shi, Xu‐Bo Zou, Guang‐Can Guo

Published Dec 1, 2016• 6 citations
Publisher

Abstract

We investigate the decoy state quantum key distribution via the atmosphere channels. We consider the efficient decoy state method with one-signal state and two-decoy states. Our results show that the decoy state method works even in the channels with fluctuating transmittance. Nevertheless, the key generation rate will be dramatically decreased by atmosphere turbulence, which sheds more light on the characterization of atmosphere turbulence in realistic free-space based quantum key distributions.

DOI
10.1088/0256-307x/33/12/120302

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We investigate the decoy state quantum key distribution via the atmosphere channels. We consider the efficient decoy state method with one-signal state and two-decoy states. Our results show that the decoy state method works even in the channels with fluctuating transmittance. Nevertheless, the key generation rate will be dramatically decreased by atmosphere turbulence, which sheds more light on the characterization of atmosphere turbulence in realistic free-space based quantum key distributions.
The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristic of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking, a procedure which is typically used in practical long-distance free-space quantum communication. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improve quantum communication.
The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristics of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking---a procedure which is typically used in practical long-distance free-space quantum communication. Eventually, we analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking not always improves quantum communication.
Reference-frame-independent quantum key distribution (RFI-QKD) has been proved to be tolerant against unknown reference frame misalignment, which reserves interesting prospects in implementing global quantum communication. However, few works have been addressed on the performance and feasibility for RFI-QKD in turbulent atmospheric channels. Here, we propose to implement RFI-QKD in practical free-space links with fluctuating transmission efficiency due to beam wandering and broadening. An improved model for estimating the probability distribution of single-photon receiving efficiency has been developed and we also simulated the Gaussian beam spot evolution and secure key rate based on that. Results show that the beam wandering model of probability distribution of transmission efficiency is reasonable to improve the performance of RFI-QKD in free-space channel.
The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement-based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD experiments. We implement a signal-to-noise ratio filter (SNRF) in our QKD system which rejects measurements during periods of low transmission efficiency, where the measured quantum bit error rate is temporarily elevated. Using this, we increase the total secret key generated by the system from 78 009 bits to 97 678 bits, representing an increase of 25.2% in the final secure key rate, generated from the same raw signals. Lastly, we present simulations of a QKD exchange with an orbiting low earth orbit satellite and show that an SNRF will be extremely useful in such a situation, allowing many more passes to extract a secret key than would otherwise be possible.
Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.
In this paper, we present a novel analysis of the feasibility of quantum key distribution between a LEO satellite and a ground station. First of all, we study signal propagation through a turbulent atmosphere for uplinks and downlinks, discussing the contribution of beam spreading and beam wandering. Then we introduce a model for the background noise of the channel during night-time and day-time, calculating the signal-to-noise ratio for different configurations. We also discuss the expected error-rate due to imperfect polarization compensation in the channel. Finally, we calculate the expected key generation rate of a secure key for different configurations (uplink, downlink) and for different protocols (BB84 with and without decoy states, entanglement-based Ekert91 protocol).