Transmitting a beam through the atmosphere over long distances can be a challenging problem. Factors from the channel, such as atmospheric turbulence causing beam wander and distortions to the wavefront, or the optical design can change the loss induced in the channel. This work simulates a quantum key distribution system implementing the BB84 protocol with entangled photons operating over a 30 km maritime channel using one, four, and nine spatial modes. For the cases of multiple spatial modes, atmospheric turbulence increases the channel cross talk, resulting in an increase in the noise for each channel. To compensate for distortions in the wavefront, adaptive optics at the transmitter or receiver are used to pre- or post-correct the wavefront.
Transmitting a beam through the atmosphere over long distances can be a challenging problem. Factors from the channel, such as atmospheric turbulence causing beam wander and distortions to the wavefront, or the optical design can change the loss induced in the channel. This work simulates a quantum key distribution system implementing the BB84 protocol with entangled photons operating over a 30 km maritime channel using one, four, and nine spatial modes. For the cases of multiple spatial modes, atmospheric turbulence increases the channel cross talk, resulting in an increase in the noise for each channel. To compensate for distortions in the wavefront, adaptive optics at the transmitter or receiver are used to pre- or post-correct the wavefront.
When using quantum key distribution (QKD), one of the trade-offs for security is that the generation rate of a secret key is typically very low. Recent works have shown that using a weak coherent source allows for higher secret key generation rates compared to an entangled photon source, when a channel with low loss is considered. In most cases, the system that is being studied is over a fiber-optic communication channel. Here a theoretical QKD system using the BB92 protocol and entangled photons over a free-space maritime channel with multiple spatial modes is presented. The entangled photons are generated from a spontaneous parametric down conversion (SPDC) source of type II. To employ multiple spatial modes, the transmit apparatus will contain multiple SPDC sources, all driven by the pump lasers assumed to have the same intensity. The receive apparatuses will contain avalanche photo diodes (APD), modeled based on the NuCrypt CPDS-1000 detector, and located at the focal point of the receive aperture lens. The transmitter is assumed to be located at Alice and Bob will be located 30 km away, implying no channel crosstalk will be introduced in the measurements at Alice’s side due to turbulence. To help mitigate the effects of atmospheric turbulence, adaptive optics will be considered at the transmitter and the receiver. An eavesdropper, Eve, is located 15 km from Alice and has no control over the devices at Alice or Bob. Eve is performing the intercept resend attack and listening to the communication over the public channel. Additionally, it is assumed that Eve can correct any aberrations caused by the atmospheric turbulence to determine which source the photon was transmitted from. One, four and nine spatial modes are considered with and without applying adaptive optics and compared to one another.
When light is propagated through a channel that is not a waveguide, such as a fiber, it is known as a free-space optical channel. When used in communication systems, free-space optical channels provide the advantages of high communication rates, lower power, and minimal infrastructure installation. When the free-space optical channel has a random medium in it, such as the atmosphere, the distortions will be applied to the phase. The phase distortions can lead to intensity fluctuations and additional beam spreading. To compensate for the distortions adaptive optics can be used, allowing for the stability of the system to be improved. Additionally, post processing techniques on transmitted data can also be used to improve the stability of the channel. By significantly decreasing the number of photons transmitted, a classical communication channel can be considered as a quantum channel. Encoding information into the quantum states of the transmitted photons, quantum communication can be performed. When transmitting on the order of 1 photon per pulse, classical post processing techniques cannot be used to improve the stability of the channel. To stabilize the free-space optical channel, adaptive optics can be used at the transmitter or receiver. As no measurement of the quantum state is performed by the adaptive optics system, no information in the photon is lost. In this work, quantum key distribution will be implemented over the quantum channel. The focus of this work is on the design and study of how the channel degradations can be overcome, as well as the establishment of a free-space optical channel with adaptive optics in a quantum networking testbed. Quantum key distribution systems were simulated over a 30 km maritime channel as well as over a underwater channel. For the 30 km channel, the use of multiple parallel spatial modes results in the highest increases of the secure key rate at the cost of transmitting a lower average number of photons. When adaptive optics is applied, the secure key rates have a small increase, however as the strength of the turbulence increases from weak to moderate, the relative improvement is higher. For the underwater channel, operation at lower depths is optimal as fewer background photons reach the receiver and the channel attenuation is lower. In the experimental setup, it was found that the single photon detectors that are being used are the limiting the channel loss to be at most 6 dB. The free space optical link established between the Electrical and Computer Engineering building and College of Optical Sciences uses a corner cube retro-reflector to yield a distance of 1.45 km. The channel has been characterized at various times of day to determine the strength of the atmospheric turbulence, which ranges from a scintillation index of 0.07 to 2.21. A classical communication experiment was performed, resulting in error-free transmission while the input power to the EDFA before the photodetector was consistently above -25 dBm.
Quantum Key Distribution (QKD) promises a provably secure method to transmit information from one party to another. Free-space QKD allows for this information to be sent over great distances and in places where fibre-based communications cannot be implemented, such as ground-satellite. The primary limiting factor for free-space links is the effect of atmospheric turbulence, which can result in significant error rates and increased losses in QKD channels. Here, we employ the use of a high-speed Adaptive Optics (AO) system to make real-time corrections to the wavefront distortions on spatial modes that are used for high-dimensional QKD in our turbulent channel. First, we demonstrate the effectiveness of the AO system in improving the coupling efficiency of a Gaussian mode that has propagated through turbulence. Through process tomography, we show that our system is capable of significantly reducing the crosstalk of spatial modes in the channel. Finally, we show that employing AO reduces the quantum dit error rate for a high-dimensional orbital angular momentum-based QKD protocol, allowing for secure communication in a channel where it would otherwise be impossible. These results are promising for establishing long-distance free-space QKD systems. High-dimensional quantum key distribution will allow for higher information density and greater error tolerance in future quantum networks. This work experimentally demonstrates how implementing an adaptive optics system in a spatial-mode free-space optical link can allow for quantum communications where it would otherwise be impossible.
The ability of an eavesdropper (Eve) to perform an intercept-resend attack on a free-space quantum-key-distribution (QKD) receiver by precisely controlling the incidence angle of an attack laser has been previously demonstrated. However, such an attack could be ineffective in the presence of atmospheric turbulence due to beam wander and spatial mode aberrations induced by the air's varying index of refraction. We experimentally investigate the impact turbulence has on Eve's attack on a free-space polarization-encoding QKD receiver by emulating atmospheric turbulence with a spatial light modulator. Our results identify how well Eve would need to compensate for turbulence to perform a successful attack by either reducing her distance to the receiver or using beam wavefront correction via adaptive optics. Furthermore, we use an entanglement-breaking scheme to find a theoretical limit on the turbulence strength that hinders Eve's attack.
This article offers a solution to the fragmentation problem through a unified model and simulation showing how Adaptive Optics (AO) improves both classical and quantum communications. Free-space optical links can carry Quantum Key Distribution (QKD) over distances that cannot be reached with fiber; however, atmospheric turbulence corrupts the wavefront. For a single-mode quantum receiver, this drives the quantum bit error rate above the security threshold before detector noise can even be considered. AO addresses this by restoring the wavefront and recovering the coupling loss. The theory, mitigation techniques, and quantum security analysis needed to understand this are spread across three research communities that rarely cite one another: atmospheric turbulence and AO theory, classical modulation over fading channels, and BB84 quantum key distribution. We consolidate and develops all three topics in order to trace the chain from wavefront error to bit error rate and secret key rate. We survey six families of turbulence mitigation and provide an assessment of their suitability for single-mode quantum links. In addition, we survey the free-space QKD experimental record, from terrestrial hops to satellite downlinks. A wave optics case study of a representative 500-km Low Earth Orbit (LEO) downlink, corrected by a closed-loop Shack–Hartmann and deformable-mirror receiver at 1.55 μm ties the review together. Across a turbulence sweep, the correction stabilizes single-mode coupling near its physical ceiling, while the uncorrected channel varies by more than an order of magnitude. When carried into the downlink budget, this lifts the quantum link across the 11% security bound at 12 of 15 turbulence conditions where the uncorrected link yields no key, thereby restoring a secure quantum bit error rate in a narrow 4.2–4.9% band throughout and a secret key rate of 7.6–11.2 kbit/s while simultaneously widening the margin of the co-propagating classical channel above its forward error correction threshold.