Integrated-optical realizations of quantum key distribution over maximally unbiased bases

Quantum key distribution (QKD) protocols based on higher order maximally unbiased bases (MUBs), potentially displaying improved range-security performance, are optically realized for higher (>2) dimensions and/or for multiple (>2) transmission and detection bases, inspired by analogies with the differential phase shift keying and pulse position modulation (PPM) formats of classical optical communication. In particular, we introduce optical realizations for: 1) a six-state protocol in qubit space, employing an extra phase modulated interferometer in the transmitter, detecting the photon in the PPM basis of three consecutive time slots and 2) a 16-state MUB protocol in four dimensions, based on differential phase encoding over four adjacent time slots. The transmitter (Alice) and receiver (Bob) for this system are realized using generalized Mach-Zehnder interferometers with four delay arms, and three phase modulators, further requiring a quantum Hadamard-4 gate, realized using four cross-connected directional couplers, to be implemented as an integrated-optical circuit. The conception and analysis of these optical realizations of abstract higher order QKD MUB-based protocols is inspired by a novel insight into the structure of the MUB set constructed by modulating a generator matrix (typically a Hadamard matrix) with a set of phasemasks. The operating characteristics of these generalized protocols are derived in terms of three simple figures of merit, the Eve detect (or Disturbance) rate, the Eve information rate, and the key creation rate