Spherical-code key-distribution protocols for qubits

Recently spherical codes were introduced as potentially more capable ensembles for quantum key distribution. Here we develop specific key-creation protocols for the two qubit-based spherical codes, the trine and tetrahedron, and analyze them in the context of a suitably tailored intercept/resend attack, both in standard form, and in a 'gentler' version whose back action on the quantum state is weaker. When compared to the standard unbiased basis protocols, Bennett-Brassard 1984 (BB84) and six-state, two distinct advantages are found. First, they offer improved tolerance of eavesdropping, the trine besting its counterpart BB84 and the tetrahedron the six-state protocol. Second, the key error rate may be computed from the sift rate of the protocol itself, removing the need to sacrifice key bits for this purpose. This simplifies the protocol and improves the overall key rate