Efficient characterization of phase relations in linear optical devices

Linear optical networks play a paramount role in current implementations of quantum information protocols using photons. A paradigmatic example of their potential is given by boson sampling experiments, which recently have reached the quantum advantage regime [1,2]. Such linear devices are essentially N-mode interferometers, whose operation is entirely captured by an N ×N unitary matrix U with complex entries uji = |uji|eθji. This matrix characterizes, in a classical framework, the transformation of the phasors εj(in) of the input field across the different modes into the phasors εj(out) of the output fields according to the linear relation (Equation presented).