Leveraging Quantum Advantage and Dimensionality in BB84-like Cryptographic Schemes

Quantum cryptography protocols take advantage of the quantum resource associated with the non-orthogonality of bases to detect an eavesdropper in a communication channel for key distribution. The BB84 protocol uses two, 2-dimensional bases with differing orientations to measure the polarization of individual photons. Implementation of this protocol results in a per-photon-sent detection probability of 25%. We increase the number of mutually non-orthogonal bases and find that the 25% detection rate holds independently of the number of bases. To understand this result, we study the effects of increasing the dimensionality to see if the quantum advantage increases. We find that, indeed, in higher dimensions, increasing the number of bases does improve detection rates. Specifically, we find a 33.33% rate for two bases in 3-dimensions compared to a 43.75% rate for three bases in 3-dimensions. We describe the methods used and interpret our results qualitatively.