Optimizing Uncertainty in Quantum Cryptography

Quantum cryptography protocols use the uncertainty multiplicity of measuring bases as a resource to detect an eavesdropper in a communication channel for key distribution. The BB84 protocol, first purposed in 1984, uses two, 2-dimensional bases with differing orientations to measure the polarization of individual photons. Implementation of this protocol results in a 25% detection rate. We increase the number of mutually non-orthogonal bases and find that the 25% detection rate holds independent of the number of bases. We then generalize the protocol to 3-dimensional qutrits and use two methods, based on Rodrigues's rotation formula and parameter optimization to find optimal basis orientation, resulting in 29.6% and 33.3% probabilities of detection. This enhancement of eavesdropper detectability is consistent with the cryptography literature.