A Radix-4 Chrestenson Gate for Optical Quantum Computation

A recently developed four-port directional coupler used in optical signal processing applications is shown to be equivalent to a radix-4 Chrestenson operator, or gate, in quantum information processing (QIP) applications. The radix-4 qudit is implemented as a location-encoded photon incident on one of the four ports of the coupler. The quantum informatics transfer matrix is derived for the device based upon the conservation of energy equations when the coupler is employed in a classical sense in an optical communications environment. The resulting transfer matrix is the radix-4 Chrestenson transform. This result indicates that a new practical device is available for use in the implementation of radix-4 QIP applications or in the construction of a radix-4 quantum computer.