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New results have been derived for wavefronts for single and multiple photons and combined with quantum hyperentanglement, multiphoton entanglement, and network properties. These new results arise from use of Lie algebra techniques for disentanglement of certain operators related to propagation. The new results include closed form exact expressions for functions related to the disentanglement process. These expressions permit many different solutions to the disentanglement process. These new expressions offer much higher order programmable self-accelerating curves to be created. This in turn facilitates more effective quantum-based sensing and communication around corners and other obstacles, with reduced loss. This approach significantly increases the information that can be communicated or stored when using a recently derived extension of superdense coding. The resulting wavefronts are shown to reduce diffraction and have the self-healing property, i.e. automatically reobtain their original form when initially damaged by turbulence. Each node of the network will transmit at least one signal and one ancilla photon in a hyper-entangled state. Parameters used for hyper-entanglement will include photon polarization, energy-time, orbital angular momentum, radial quantum number, etc. as well as up to 12 parameters characterizing the wavefront properties. Eigenfunctions of operators associated with each 2D paraxial wave equation will be determined each being a function of up to six parameters. The same wavefront or combinations of wavefronts can be applied to multiple photons to combine hyper-entanglement with multiphoton entanglement offering additional improvements. Measures of effectiveness such as the signal-to-noise ratio (SNR), measurement time, resolution measures, and Holevo bound are considered.
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