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This invention addresses a key challenge in quantum communication networks by developing a controlled-NOT (CNOT) gate that operates between two degrees of freedom (DoFs) within a single photon: polarization and frequency.

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This invention is directed to a machine leaning methodology to quantify the association of a set of input variables to a set of output variables, specifically for the one-to-many scenarios in which the output exhibits a range of variations under the same replicated input condi