Quantum Process Calculus for Linear Optical Quantum Computing

We extend quantum process calculus in order to describe linear optical elements. In all previous work on quantum process calculus a qubit was considered as the information encoded within a 2 dimensional Hilbert space describing the internal states of a localised particle, most often realised as polarisation information of a single photon. We extend quantum process calculus by allowing multiple particles as information carriers, described by Fock states. We also consider the transfer of information from one particular qubit realisation (polarisation) to another (path encoding), and describe post-selection. This allows us for the first time to describe linear optical quantum computing (LOQC) in terms of quantum process calculus. We illustrate this approach by presenting a model of an LOQC CNOT gate.