Toward Universal Transformations of Orbital Angular Momentum of a Single Photon

High-dimensional quantum systems offer many advantages over low-dimensional quantum systems. Meanwhile, unitary transformations on quantum states are important parts in various quantum information tasks, whereas they become technically infeasible as the dimensionality increases. The photonic orbital angular momentum (OAM), which is inherent in the transverse spatial mode of photons, offers a natural carrier to encode information in high-dimensional spaces. However, it is even more challenging to realize arbitrary unitary transformations on the photonic OAM states. Here, by combining the path and OAM degrees of freedom of a single photon, an efficient scheme to realize arbitrary unitary transformations on the path-OAM coupled quantum states is proposed. The proposal reduces the number of required interferometers by approximately one quarter compared with previous works, while maintaining the symmetric structure. It is shown that by using OAM-to-path interfaces, this scheme can be utilized to realize arbitrary unitary transformations on the OAM states of photons. This work facilitates the development of high-dimension quantum state transformations and opens a new door to the manipulation of the photonic OAM states.

Automated summary

High-dimensional quantum systems have advantages over low-dimensional ones, but unitary transformations on quantum states become technically infeasible as the dimensionality increases. Photonic orbital angular momentum (OAM) provides a natural carrier to encode information in high-dimensional spaces. This work proposes an efficient scheme to realize arbitrary unitary transformations on the path-OAM coupled quantum states by combining the path and OAM degrees of freedom of a single photon. It reduces the number of required interferometers while maintaining the symmetric structure, and can be used to manipulate the photonic OAM states.