[Paper Review] Quantum Key Distribution Using Multiple Gaussian Focused Beams

Boulat A. Bash, Nivedita Chandrasekaran+2 more|arXiv (Cornell University)|Apr 28, 2016

Orbital Angular Momentum in Optics16 references3 citations

TL;DR

This paper proposes an overlapping Gaussian beam array (OGBA) architecture for free-space quantum key distribution (QKD) in the near-field regime, using multiple spatially multiplexed focused Gaussian beams with optimized beam width, intensity, and receiver pixel geometry. The OGBA achieves key rate improvements within 2.6 dB of the theoretical maximum using orbital-angular-momentum (OAM) modes, but with significantly lower hardware complexity and cost, offering a practical alternative for metropolitan and maritime QKD links.

ABSTRACT

The secret key rate attained by a free-space QKD system in the {\em near-field} propagation regime (relevant for $1$-$10$ km range using $\approx 7$ cm radii transmit and receive apertures and $1.55~μ$m 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.

Motivation & Objective

• To investigate whether non-OAM spatial modes can achieve similar QKD rate gains as OAM modes in the near-field free-space propagation regime.
• To determine if orthogonal spatial modes are necessary for spatial-multiplexing gain or if simpler beam profiles suffice.
• To design and evaluate a practical OGBA architecture that maximizes key rate using overlapping focused Gaussian beams and pixelated detectors.
• To compare the performance of OGBA against OAM-mode-based systems in terms of achievable key rate and hardware complexity.
• To assess the potential for further performance gains using non-square beam packing (e.g., hexagonal packing) and to explore extension to continuous-variable QKD.

Proposed method

• The OGBA architecture uses an array of focused Gaussian beams transmitted through a hard-pupil square aperture, with beam width, intensity, and receiver pixel geometry optimized for maximum key rate.
• The receiver employs a pixelated single-photon detector array with unity fill factor, where each beam is focused at the center of a detector pixel, and beam offset is optimized for the 1×2 configuration.
• The system models free-space propagation in the near-field regime (D_f >> 1), where multiple spatial modes can achieve near-unity transmissivity (η ≈ 1), enabling spatial multiplexing gain proportional to D_f.
• Key rate is computed using the direct-transmission QKD capacity formula for a lossy bosonic channel, with the total rate scaled by the number of effective spatial modes.
• The performance is benchmarked against ideal OAM-mode systems (infinite modes) and state-of-the-art experimental OAM separation (25 modes), accounting for mode-sorting inefficiencies.
• Optimal parameters (beam width, intensity, pixel size, beam offset) are derived and plotted as functions of link distance, with results validated for 1 km links at 1.55 µm wavelength.

Experimental results

Research questions

• RQ1 Can non-OAM spatial modes such as focused Gaussian beams achieve comparable QKD key rate gains to OAM modes in the near-field regime?
• RQ2 Is the use of orthogonal spatial modes necessary to achieve spatial-multiplexing gain in QKD, or can simpler beam profiles suffice?
• RQ3 How does the key rate performance of an OGBA architecture compare to that of OAM-mode-based systems, both theoretically and with current experimental mode-sorting capabilities?
• RQ4 What is the impact of beam geometry, overlap, and detector pixel configuration on the achievable key rate in OGBA systems?
• RQ5 Can OGBA outperform or match OAM-based systems in terms of key rate while significantly reducing hardware complexity and cost?

Key findings

• The OGBA architecture achieves a key rate improvement of 1 to 2 orders of magnitude over single-mode QKD in a 1 km free-space link using 7 cm aperture radii at 1.55 µm wavelength.
• The OGBA system achieves up to 6.3 dB less key rate loss than the theoretical maximum using all azimuthal OAM modes, indicating near-optimal spatial-multiplexing performance.
• With current state-of-the-art OAM mode separation (25 modes), the OGBA system outperforms OAM-based QKD by up to 2.6 dB in key rate, even without accounting for additional losses in mode sorting.
• The optimal beam width, intensity, and detector pixel size are found to be range-dependent, with beam width and intensity increasing with link distance to maintain high transmissivity.
• The OGBA performance is robust and could improve further with hexagonal beam packing, though this was not explored in the current study.
• The OGBA architecture offers a practical, low-complexity alternative to OAM-based systems, with comparable key rate performance but significantly reduced hardware cost and complexity.