Optical realization of universal unitary operation of single partite polarization encoded qudit

Abstract

How to generate and manipulate high dimensional quantum state is a hot topic in the area of quantum information processing. In the optical system, based on the technique of linear optics and cross phase modulation, we consider the realization of universal unitary operation of single partite polarization encoded qudit. Firstly, we introduce the spatially encoded qudit as ancilla, and the entangler of polarization encoded qudit and spatially encoded qudit as core element. After that, the realization of a special unitary operation for single qutrit is discussed by one entangler and the Fourier transformation performed on the spatially encoded qutrit by a linear optical multi-port interferometer (LOMI). The corresponding success probability could be high, but this scheme is only available for a special type of unitary operations and cannot be developed to realize higher dimensional unitary operation. For general qudit universal unitary operation realization, we use qutrit unitary operation as example. The polarization encoded qutrit could be transformed to spatially encoded qutrit by one entangler and the measurement of polarization encoded qutrit, associated with the measurement results are used to control the transmission factors of mirrors placed on the spatial modes of spatially encoded qutrit. Then the desired universal unitary operation is performed on spatially encoded qutrit by a LOMI. Finally, one more entangler, a LOMI implementing Fourier transformation to spatially encoded qutrit, the measurement of spatially encoded qutrit and the phase shifts controlled by the measurement results through classical feed-forward will complete the realization of qutrit unitary operation. This approach could be developed for general case. By two entanglers, one LOMI for Fourier transformation of spatially encoded qudit and the measurement of polarization encoded qudit associated with its results are used to control the transmission factors of mirrors, the bi-directional mapping between polarization and spatially encoded qudits could be realized. Therefore, the universal unitary operation for general qudit could be realized by one more LOMI performed on the ancilla spatially encoded qutrit. In principle, our scheme is available for general single partite polarization encoded qudit and is feasible with the current experimental technology.