  Quantum key distribution (QKD) has long been a promising area for application
of quantum effects toward solving real-world problems. But two major obstacles
have stood in the way of widespread applications: low secure key generation
rates and short achievable operating distances. In this paper, a new physical
mechanism for dealing with the first of these problems is proposed: interplay
between different degrees of freedom in a hyperentangled system (parametric
down conversion) is used to increase the Hilbert space dimension available for
key generation while maintaining security. Polarization-based Bell tests
provide security checking, while orbital angular momentum (OAM) and total
angular momentum (TAM) provide higher key generation rate. Whether to measure
TAM or OAM is decided randomly on each trial. The concurrent non-commutativity
of TAM with OAM and polarization provides the physical basis for quantum
security. TAM measurements link polarization to OAM, so that if the legitimate
participants measure OAM while the eavesdropper measures TAM (or vice-versa),
then polarization entanglement is lost, revealing the eavesdropper. In contrast
to other OAM-based QKD methods, complex active switching between OAM bases is
not required; instead, passive switching by beam splitters combined with much
simpler active switching between polarization bases makes implementation at
high OAM more practical.
