Abstract
We propose compact three-dimensional photonic circuit designs that guarantee a remarkable reduction in the complexity of circuits to perform quantum state tomography of N-dimensional path qudits. We obtain solutions such that the number of beam splitters obeys a polynomial function of degree three with the quantum system dimension, whereas, in current proposals, this quantity grows with a polynomial function of degree four. In addition, the optical depth reduces from quadratic to linear over the dimension of the Hilbert space.
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