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Quantum key distribution over free space optic (FSO) channel using higherorder Gaussian beam spatial modes

Quantum key distribution (QKD) has emerged as a secure solution of secret key distribution utilizing the well established theories of modern physics. Since its introduction in 1984, many interesting and innovative ideas have been proposed for QKD in order to improve the security and efficiency of the scheme keeping in view of its applications and practical implementation. High error rate QKD scheme for long distance communication – the so-called KMB09 protocol – is one such scheme which was designed to achieve longer communication distance in QKD, without compromising its security, by allowing the utilisation of higher dimensional photon states which is not possible with standard BB84 scheme. However the practical implementation of KMB09 protocol has not been presented yet because of its unique design. In this paper, we propose a framework for the practical implementation of QKD system that runs KMB09 protocol in two or more dimensions of photon states. We present the KMB09 based QKD system design and its simulation for practical implementation based on the encoding of secret bits in higher order Gaussian beam spatial modes. The proposed framework is specifically evaluated in terms of efficiency or success rate with two and four dimensions of photon states. We find that the simulation results of the proposed framework are inline with the numerical and analytical results of the same QKD model presented earlier.