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Physical Review A

Characterization and mitigation of information loss in a six-state quantum-key-distribution protocol with spatial modes of light through turbulence

Bienvenu I. Ndagano, Andrew Forbes

Published Dec 26, 2018• 22 citations
Publisher

Abstract

Quantum communication with structured photons is topical, owing to the multidimensional state space of spatial modes. However, spatial modes are fragile and their quality degrades when perturbed in traditional communication media such as free-space and optical fibers. Here, we illustrate the effects of atmospheric turbulence on a six-state quantum-key-distribution protocol with orbital angular momentum (OAM) modes. We experimentally characterize the fidelity decay as a function of turbulence strength, showing a concomitant decrease with increasing perturbation, and consider the influence of both mode order and mode size, showing that OAM modes with higher helicity are more resilient to turbulence for this protocol. We outline two approaches to mitigate the photon information loss. In the first, we show that by postselecting on a high-dimensional subspace at the detection side, we can recover information contained in the scattered modes. In the second, we measure the channel operator by means of classically entangled light and mitigate errors on the quantum state through entanglement concentration by means of one-party Procrustean filtering. The tools we provide here will be beneficial for realizing more robust quantum communication with OAM modes of light.

DOI
10.1103/physreva.98.062330

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Quantum communication with structured photons is topical, owing to the multidimensional state space of spatial modes. However, spatial modes are fragile and their quality degrades when perturbed in traditional communication media such as free-space and optical fibers. Here, we illustrate the effects of atmospheric turbulence on a six-state quantum-key-distribution protocol with orbital angular momentum (OAM) modes. We experimentally characterize the fidelity decay as a function of turbulence strength, showing a concomitant decrease with increasing perturbation, and consider the influence of both mode order and mode size, showing that OAM modes with higher helicity are more resilient to turbulence for this protocol. We outline two approaches to mitigate the photon information loss. In the first, we show that by postselecting on a high-dimensional subspace at the detection side, we can recover information contained in the scattered modes. In the second, we measure the channel operator by means of classically entangled light and mitigate errors on the quantum state through entanglement concentration by means of one-party Procrustean filtering. The tools we provide here will be beneficial for realizing more robust quantum communication with OAM modes of light.
We describe an experimental implementation of a free-space 11-dimensional communication system using orbital angular momentum (OAM) modes. This system has a maximum measured OAM channel capacity of 2.12 bits/photon. The effects of Kolmogorov thin-phase turbulence on the OAM channel capacity are quantified. We find that increasing the turbulence leads to a degradation of the channel capacity. We are able to mitigate the effects of turbulence by increasing the spacing between detected OAM modes. This study has implications for high-dimensional quantum key distribution (QKD) systems. We describe the sort of QKD system that could be built using our current technology.
Quantum key distribution is a promising candidate to ensure secure communication in the future. Higher-dimensional state spaces as provided by the orbital angular momentum of photons (OAM) could further improve the security and robustness to noise. When transmitted through free-space, these photons experience atmospheric turbulence which introduces distortions to the encoded OAM. A technologoy called adaptive optics has been developed in astronomy to counter-act turbulence-induced distortion. While the application of adaptive optics has been considered in the context of classical OAM communication, this thesis presents the first results for OAM-based quantum key distribution. The main result of this thesis is that the losses of the quantum mechanical properties of OAM photons in atmospheric can be mitigated by adaptive optics. Both the entanglement and the trace of the final state's density matrix can be significantly improved. Furthermore, the security of the quantum key distribution protocol can be ensured for two to three times stronger turbulence as measured by the Fried parameter. The presented results demonstrate the great potential of adaptive optics for OAM quantum cryptography.
Quantum key distribution (QKD) technology has demonstrated remarkable practicality and sustained developmental trends in the current field of quantum communication. This paper focuses on a novel and potent quantum communication protocol, specifically quantum key distribution utilizing the encoding of information through orbital angular momentum (OAM) of photons. OAM states, owing to their distinctive properties, exhibit significant advantages in terms of information capacity and channel robustness. However, the sensitivity of OAM states to atmospheric conditions and challenges arising from wavefront distortions necessitate in-depth investigation. Additionally, the unique structure of OAM beams has raised concerns about geometric losses. By analyzing the impact of atmospheric turbulence and geometric losses on the transmission performance when applying the OAM-QKD protocol in free space, this paper explores variations in system losses under different OAM orders. Simulation results indicated that as the channel distance increases, system losses gradually escalate. Furthermore, with an increase in OAM order, although the system's sensitivity to atmospheric turbulence diminishes, geometric losses exhibit an exponential increase. Addressing this issue, our research suggested that when considering free-space quantum key distribution with OAM encoding, selecting an OAM order of 1 for the beam achieves minimal transmission losses. Therefore, in practical applications, employing OAM beams with <?TeX l=1l = 1l=1 ?> emerges as an effective strategy to optimize the performance of the OAM-QKD protocol in free space.
The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge in OAM QKD systems operating over free-space communication channels. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that even though our AO system provides a limited correction, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel. The crosstalk induced by turbulence and the performance of AO systems is investigated in two configurations: a lab-scale link with controllable turbulence, and a 340 m long cross-campus link with dynamic atmospheric turbulence. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing, and accurate wavefront correction is necessary to adequately correct turbulence-induced error. We also propose and demonstrate different solutions to improve the performance of OAM QKD with turbulence, which could enable the possibility of OAM encoding in strong turbulence.
Quantum key distribution (QKD) employed orbital angular momentum (OAM) for high-dimensional encoding enhances the system security and information capacity between two communication parties. However, such advantagesare significantly degraded because of the fragility of OAM states in atmospheric turbulence. Unlike previous researches, we first investigate the performance degradation of OAM-based QKD by infinitely long phase screen (ILPS), which offers a feasible way to study how adaptive optics (AO) dynamically corrects the turbulence-induced aberrations in real time. Secondly, considering the failure of AO while encountering phase cuts, we evaluate the quality enhancement of OAM-based QKD under a moderate turbulence strength by AO after implementing the wrapped cuts elimination. Finally, we simulate that, with more realistic considerations; real-time AO can still mitigate the impact of atmospheric turbulence on OAM-based QKD even in the large wind velocity regime.
Abstract In the last two decades, structured light patterns with orbital angular momentum (OAM) have been extensively utilized in quantum cryptography or quantum key distribution, which is generally considered an unconditionally secure method of secret key transmission between two distant communicating entities. High-dimensional encoding of quantum bits in quantum key distribution improves the security and information-carrying capability of a quantum signal. Significant degradation in the efficiency of such communication is observed due to the aberration of OAM states under atmospheric turbulence. In this paper, we focus on analyzing the impact of atmospheric turbulence on the error-rates of quantum key distribution, which is considered the benchmark in analyzing the security of such communication over the quantum channel in the presence of an intruder (man-in-the-middle). Our results show that turbulence under normal conditions does not significantly affect the successful transmission of secret quantum bits between sender and receiver. Furthermore, we identify an interesting variation in the signature of error-rates to clearly detect the presence of an intruder as a result of medium-level turbulence.