Efficient Characterization of Phase Relations in Linear Optical Devices

Abstract

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$N\times N$unitary matrix$U$with complex entries$u_{j i}=\left\vert u_{j i}\right\vert e^{\theta_{j i}}$. This matrix characterizes, in a classical framework, the transformation of the phasors$\varepsilon_{j}^{(in)}$of the input field across the different modes into the phasors$\varepsilon_{j}^{(out)}$of the output fields according to the linear relation$\varepsilon_i^{({out })}=\sum_i u_{j i} \varepsilon_i^{({in })}$).