## High Capacity Quantum Key Distribution via Hyper-Entangled Degrees of Freedom    [PDF]

David S. Simon, Alexander V. Sergienko
A new method is proposed for increasing the Hilbert space dimension $N$ available for quantum key distribution in such a way that the complexity of the required apparatus increases much more slowly with $N$ than in other currently used protocols. The key idea is to use a hyperentangled system in which one entangled degree of freedom is used for key generation, and a \emph{different} degree of freedom is used for security checking. For this to work, it is necessary that the two degrees of freedom be mutually commuting, allowing them to be simultaneously measured. A system that satisfies the necessary requirements is paraxial (near-collinear) parametric down conversion, with polarization used for security checking and orbital angular momentum (OAM) for key generation. Two variations are given. The first allows the same photons to be used for both key generation and security checking; many fewer photons are lost from the key generation process, greatly increasing the efficiency. This gain comes at the expense of the eavesdropper being able to gain full information of the OAM state, although her actions can be detected. The second variation sacrifices the ability to use the same photons for security and key generation, but in return reduces the amount of information the eavesdropper can gain.
View original: http://arxiv.org/abs/1306.3489