Entanglement in a Twist: The strong correlations observed in quantum mechanically entangled particles, such as photons, offer potential for secure communication and quantum information processing. Leach et al. (p. 662 ) now show such strong quantum correlations between the complementary variables—angular position and orbital angular momentum—of two photons created during the parametric down-conversion process in a nonlinear crystal. This demonstration of entanglement in an angular basis establishes that angles are genuine quantum observables and can therefore be considered a resource for quantum information processing, capable of secure, high-dimension, key distribution.

A beam with an angular-dependant phase $\mathrm{\Phi }=\ell \varphi$ about the beam axis carries an orbital angular momentum of $\ell \hslash$ per photon. Such beams are exploited to provide superresolution in microscopy. Creating extreme ultraviolet or soft-x-ray beams with controllable orbital angular momentum is a critical step towards extending superresolution to much higher spatial resolution. We show that orbital angular momentum is conserved during high-harmonic generation. Experimentally, we use a fundamental beam with $|\ell |=1$ and interferometrically determine that the harmonics each have orbital angular momentum equal to their harmonic number. Theoretically, we show how any small value of orbital angular momentum can be coupled to any harmonic in a controlled manner. Our results open a route to microscopy on the molecular, or even submolecular, scale.

In this work, it is experimentally demonstrated that the nonseparability of vector beams (e.g., radial and azimuthal polarization) can be used to encode information for optical communication. By exploiting the nonseparability of a vector beam’s space and polarization degrees of freedom using conventional wave plates, it is shown that 2 bits of information can be encoded when applying the identity and three Pauli operators to its polarization degree of freedom. It is also shown that vector beams can be efficiently decoded with as low as 2.7% cross talk using a Mach–Zehnder interferometer that exploits a higher-order Pancharatnam–Berry phase and liquid crystal $q$-plates.

We describe an experimental implementation of a free-space 11-dimensional communication system using orbital angular momentum (OAM) modes. This system has a maximum measured OAM channel capacity of 2.12 bits/photon. The effects of Kolmogorov thin-phase turbulence on the OAM channel capacity are quantified. We find that increasing the turbulence leads to a degradation of the channel capacity. We are able to mitigate the effects of turbulence by increasing the spacing between detected OAM modes. This study has implications for high-dimensional quantum key distribution (QKD) systems. We describe the sort of QKD system that could be built using our current technology.