Linear-optics realization of channels for single-photon multimode qudits

We propose and theoretically study a method for the stochastic realization of arbitrary quantum channels on multimode single-photon qudits. In order for our method to be undemanding in its implementation, we restrict our analysis to linear-optical techniques, vacuum ancillary states, and nonadaptive schemes, but we allow for random switching between different optical networks. With our method it is possible to deterministically implement random-unitary channels and to stochastically implement general channels. We provide an expression for the optimal probability of success of our scheme and calculate this quantity for specific examples such as the qubit amplitude-damping channel. The success probability is shown to be related to the entanglement properties of the Choi-Jamiolkowski state isomorphic to the channel.