High Capacity Quantum Key Distribution via Hyper-Entangled Degrees of Freedom

Abstract: 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.