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.
Highlights
Within the past few decades the orbital angular momentum (OAM) modes have received extensive attention [1,2,3,4,5] and are widely applied in various information technologies, including quantum teleportation [6], optical communications [7], and quantum key distribution [8,9,10]
The OAM modes only account for azimuthal variations in the transverse plane, and it has been shown that these modes cannot reach the capacity limit of a communications link without including the radial degree of freedom [11]
The LG modes are characterized by a radial quantum number p and an OAM quantum number, and arbitrary paraxial field can be described by these modes [12]
Summary
Within the past few decades the orbital angular momentum (OAM) modes have received extensive attention [1,2,3,4,5] and are widely applied in various information technologies, including quantum teleportation [6], optical communications [7], and quantum key distribution [8,9,10]. It is apparent that the transmission rate of a communications system can be further increased by using both azimuthal and radial degrees of freedom, and it has been shown that the radial index p can potentially mitigate the power loss when the receiver has a limited aperture size [14]. Recent advances have shown how to efficiently measure and use p and in optical communications [19,20,21,22,23,24,25,26], but the mode sorting in mutually unbiased basis of LG modes required by a quantum key distribution (QKD) protocol has not previously been reported. In the following we present how to build a superposition mode sorter and provide the experimental demonstration of a QKD protocol employing all three transverse degrees of freedom
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