| CPC H04L 9/0852 (2013.01) [H04L 9/0869 (2013.01)] | 16 Claims | 

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               1. A key generator system, comprising: 
            a photon source configured to generate a spin-1 particle; 
                an N-dimensional quantum random number generator (ND-QRNG) including: 
                an optical unit including: 
                  a preparation stage configured to enable certification via value indefiniteness; and 
                    a measurement stage configured to generate numbers and outcomes attained by measuring a state of a particle utilized to prepare an N-dimensional quantum system in a state that satisfies a set of conditions that guarantees there is no definite value associated to the measurement outcome; and 
                  a detector configured to output a sequence of N-ary numbers; 
                a processor; and 
                a memory, including instructions stored thereon, which, when executed by the processor cause the system to: 
              generate, by the photon source, a spin-1 particle; 
                  receive the spin-1 particle by the optical unit; 
                  generate by the optical unit a set of outcomes based on the state of the spin-1 particle; 
                  detect by the detector the set of outcomes; and 
                  output by the detector a sequence of N-ary numbers based on the detected set of outcomes; 
                  wherein the instructions, when executed by the processor, further cause the measurement stage to: 
                receive one or more photons on at least one input port of a universal interferometer of the measurement stage of the optical unit; and 
                    measure, using N(N−1)/2 two-dimensional (2D) interferometers of the universal interferometer of the measurement stage, along a Hermitian Unitary operator of a Cartesian coordinate standard system the one or more photons prepared by the preparation stage and preserving three dimensions of quantum information in a Hilbert space of the received one or more photons. 
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