M.Sc Thesis

M.Sc StudentTselniker Igor
SubjectMutually Unbiased Bases with Application to Optical
Realizations of Quantum Key Distribution
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Moshe Nazarathy


In this work Quantum Key Distribution (QKD) protocols, based on higher-order MUBs (Mutually Unbiased Bases), 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 DPSK (Differential Phase Shift Keying) formats of classical optical communication.

This thesis is based on and further develops two central concepts:

(i) The abstract mathematical concept of Mutually Unbiased Bases (MUB), used to account for the operation of advanced QKD protocols using multiple (>4) states in multiple (>2) dimensions, generalizing the well-known BB84 protocol. (ii) Optical and Integrated-Optical Differential-Phase-Shift-Keying (DPSK) based realizations implementations of the generalized QKD protocol mentioned above, based on phase encoding.

We design for the first time, MUBs compatible with quaternary DPSK transmission. Under this constraint, we identify a group-theoretic structure of the MUB set, which forms a subgroup of the DPSK group. 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 Hadamard matrix with a set of phasemasks.

This lays the foundation for elegant integrated-optical implementations, based on elements such as the Hadamard-gate, phase modulators, and tapped delay lines. In particular, we introduce a realization of 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 phase modulators, further requiring a quantum Hadamard-4 gate component, for which we provide a novel realization using four cross-connected directional couplers, to be implemented as an integrated-optical circuit.

The operating characteristics (OC) of these generalized protocols are derived in terms of three simple figures of merit, the Eavesdropper Detect (or Disturbance) Rate (EDR), the Eavesdropper Information Rate (EIR) and the Key Creation Rate (KCR).

We finally propose an abstract realization of the generalized MUB-based QKD protocol, whereby Alice emits multiple photons in various, possibly entangled states, encoding the MUB vectors, with the entanglement effected using control-phase gates, and with Bob utilizing a similar apparatus.