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Conference on Lasers and Electro-Optics

Performance Analysis of Free-space Quantum Key Distribution Using Multiple Spatial Modes

Wenhua He, Saikat Guha, Jeffrey H. Shapiro, Boulat A. Bash

Published Jan 1, 2021• 0 citations
Publisher

Abstract

We present a flat-top focused-beam spatial multiplexing scheme for quantum key distribution. It captures a significant fraction of the multiplexing rate gain in vacuum transmission, and outperforms OAM-bearing modes in turbulence.
DOI
10.1364/cleo_qels.2021.ftu1n.7

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In the diffraction-limited near-field propagation regime, free-space optical quantum key distribution (QKD) systems can employ multiple spatial modes to improve their key rate. This improvement can be effected by means of high-dimensional QKD or by spatial-mode multiplexing of independent QKD channels, with the latter, in general, offering higher key rates. Here, we theoretically analyze spatial-mode-multiplexed, decoy-state BB84 whose transmitter mode set is either a collection of phase-tilted, flat-top focused beams (FBs) or the Laguerre-Gaussian (LG) modes. Although for vacuum propagation the FBs suffer a QKD rate penalty relative to the LG modes, their potential ease of implementation make them an attractive alternative. Moreover, in the presence of turbulence, the FB modes may outperform the LG modes.
The secret key rate attained by a free-space QKD system in the {\em near-field} propagation regime (relevant for 111-101010 km range using ≈7\approx 7≈7 cm radii transmit and receive apertures and 1.55 μ1.55~μ1.55 μm transmission center wavelenght) can benefit from the use of multiple spatial modes. A suite of theoretical research in recent years have suggested the use of orbital-angular-momentum (OAM) bearing spatial modes of light to obtain this improvement in rate. We show that most of the aforesaid rate improvement in the near field afforded by spatial-mode multiplexing can be realized by a simple-to-build overlapping Gaussian beam array (OGBA) and a pixelated detector array. With the current state-of-the-art in OAM-mode-sorting efficiencies, the key-rate performance of our OGBA architecture could come very close to, if not exceed, that of a system employing OAM modes, but at a fraction of the cost.
In this paper, a free-space quantum key distribution (QKD) system based on BB84 protocol is studied assuming that the transmitted quantum bits are multiplexed spatially based on orthogonal orbital angular momentum (OAM) carrying beams. The performance of such a system is estimated in terms of quantum bit error rate, outage capacity, and effective data rate taking into account the impact of error correction and privacy amplification. Based on the simulation of OAM-carrying beam propagating through atmospheric channels impaired by turbulence, the crosstalk among the multiplexed channels are investigated and its effect on the performance of the QKD system is evaluated. The presented results provide insight into the efficient design of such multiplexed QKD systems particularly in terms of the choice of the optimal average photon number per pulse and the multiplexing mode set.
High-dimensional quantum key distribution (HD-QKD) provides notable advantages over qubit-based QKD, including higher key rates and greater noise resilience. Leveraging the orbital angular momentum states of structured photons to encode information has become a prominent method for implementing HD-QKD. However, practical challenges such as state-dependent diffraction, limited receiving aperture, and atmospheric turbulence impose constraints on the attainable performance and encoding dimension of QKD in free-space links. In this work, we address these challenges with focused, structured photons. Numerical simulations indicate that this method markedly enhances transmission efficiency and improves the robustness against turbulence, resulting in higher key rates and extended transmission distances in free-space HD-QKD. Additionally, focused, structured photons allow us to implement higher-dimensional QKD and enable QKD systems to achieve superior performance with smaller receiving apertures in a turbulent free-space link. This makes our approach particularly advantageous for applications of unmanned aerial vehicles and satellite platforms. Our work contributes to exploring the robust QKD schemes employing structured photons and may promote its application in quantum networks.
Continuous-Variable Quantum Key Distribution (CVQKD), based on quantum mechanical principles, offers theoretically unconditional security and represents a crucial direction for future secure communications. However, its application in marine environments faces challenges such as high attenuation, scattering, and turbulence in seawater, severely impacting quantum signal transmission and secure key generation efficiency. Orbital angular momentum (OAM) multiplexing technology leverages the orthogonality of photon OAM modes to transmit multiple independent quantum signals in parallel within a single spatial channel. In this scheme, each OAM mode serves as an independent sub-channel, enabling simultaneous key distribution across multiple modes, thereby significantly enhancing the system’s secure key rate and spectral efficiency. This paper proposes an OAM-multiplexed CVQKD scheme tailored for marine channels. Based on Yi’s power spectrum model for marine turbulence refractive index fluctuations, we derive expressions for OAM mode probability density and detection probability. Through system modeling and performance analysis, we investigate the impact of marine turbulence on OAM modes, as well as on the secure key rate and transmission distance of CVQKD systems. Results indicate that higher-order OAM modes exhibit more pronounced turbulence effects, leading to reduced key rates and limited transmission distances. The OAM multiplexing approach significantly enhances system key rates, providing theoretical and technical references for constructing high-rate seawater quantum communication networks.