The simulation and analysis of a hyperentangled photon source based on polarization and transverse momentum are achieved using the MATLAB platform. The analysis includes determining the emission pattern of a spontaneous parametric down-conversion source and the opening angles of emission cones and their dependence on wavelength. The energy conservation in the generation process and the correlations between the hyperentangled states are investigated. The results show that the generated states are maximally entangled, and Bell’s inequality test is proven to satisfy the theoretical limits. The proposed model gives better insight into the generation process of hyperentangled photons. It could be integrated with simulations of any arbitrary system based on a hyperentangled source.
A full quantum secure direct communication system is implemented in MATLAB environment using linear optical devices and single-photon detectors. MATLAB has the advantage of integrating the simulation of the whole system, which has optical and electronic blocks, all together into one script. Each block of the system (transmitter, receiver, and security check) is physically and mathematically explained, and the idea behind the code is presented. Results from running the whole simulation are in accordance with those obtained either from the published practical systems or from using state-of-the-art commercially available optical simulators. Our approach opens the way to simulate with confidence hyperentangled systems where experimental data are not yet widely available.
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