Using all transverse degrees of freedom in quantum communications based on a generic mode sorter

TL;DR

This paper introduces a versatile mode sorter capable of measuring superpositions of Laguerre-Gaussian modes, enabling 8-dimensional quantum key distribution using all three transverse degrees of freedom of photons, thus enhancing free-space communication capacity.

Contribution

The authors develop and demonstrate a generic mode sorter that sorts superpositions of LG modes, incorporating radial modes into quantum communication protocols for the first time.

Findings

Achieved 8-dimensional quantum key distribution using all three transverse degrees of freedom.

Demonstrated efficient measurement of superpositions of LG modes with a mode converter.

Enhanced potential capacity of free-space quantum communication links.

Abstract

The dimension of the state space for information encoding offered by the transverse structure of light is usually limited by the finite size of apertures. The widely used orbital angular momentum (OAM) number of Laguerre-Gaussian (LG) modes in free-space communications cannot achieve the theoretical maximum transmission capacity unless the radial degree of freedom is multiplexed into the protocol. While the methodology to sort the radial quantum number has been developed, the application of radial modes in quantum communications requires an additional ability to efficiently measure the superposition of LG modes in the mutually unbiased basis. Here we develop and implement a generic mode sorter that is capable of sorting the superposition of LG modes through the use of a mode converter. As a consequence, we demonstrate an 8-dimensional quantum key distribution experiment involving all three transverse degrees of freedom: spin, azimuthal, and radial quantum numbers of photons. Our protocol presents an important step towards the goal of reaching the capacity limit of a free-space link and can be useful to other applications that involve spatial modes of photons.