Implementation of photon partial distinguishability in a quantum optical circuit simulation

This paper presents a method to implement partial distinguishability between photons in a simulation of an arbitrary optical quantum circuit. The continuous degrees of freedom of the photons are represented by wavepackets which contain information of their time and frequency distributions. In order to account for partial distinguishability of photons, we increase the number of degrees of freedom associated with the circuit operation. We also reduce the infinite wavepacket configurations to a discrete subset where each different photon wavepacket is labeled by an integer index that can be treated in the same footing as the rest of the circuit quantum numbers. This allows to define a delay operation in the same matrix formalism used for any other linear operation of a quantum circuit.