published_or_final_version / Physics / Doctoral / Doctor of Philosophy

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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Quantum key distribution (QKD) aims at the creation of a secret key in the two locations of partners, traditionally Alice and Bob, wishing to communicate in private. A generic QKD protocol utilises a quantum channel and an authenticated classical channel for exchanges between partners in Phases 1 and 2 of the protocol, respectively. Phase 1 can be described as a prepareand- measure (P&M) or equivalently as an entanglement-based (EB) phase. Bob performs the same measurement in both descriptions. Subsequent to measurement, Phase 2 is commenced, the aim of which is to distill a secret key from the measurement outcomes resulting from Phase 1. A necessary condition for the security of a QKD protocol is that the measurement performed by Bob in Phase 1 must be described by non-commuting POVM elements. One method of proving the unconditional security of a QKD protocol is to show that the complete protocol (including Phases 1 and 2) is equivalent to an entanglement distillation protocol. A rst step towards showing such an equivalence for a given P&M QKD protocol is to describe an EB translation of Phase 1, where the condition on Bob's measurement is met. Di erential-phase-shift (DPS) QKD is a member of the class of distributedphase- reference QKD protocols. Unconditional security proofs for this class of protocols do not yet exist. Phase 1 of DPSQKD is here described and formalised as both a P&M and an EB phase, and Bob's measurement is shown to be described by non-commuting POVM elements. This description of an equivalent EB translation of DPSQKD where the condition on Bob's measurement is met, is a fi rst step towards a potential unconditional security proof for the protocol based on entanglement distillation. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.

The Wigner formalism can be used to provide a representation of quantum dynamics in a classical-like phase space. However, there are many cases, such as when dealing with spin systems in a dissipative environment, in which one can more conveniently resort to a partial Wigner representation. The quantum propagator in the partial Wigner representation is, in general, a very complicated mathematical object. However, using a linear approximation, the propagator can be taken as a basis for describing the dynamics of hybrid quantum-classical systems. Such a hybrid system is composed of a quantum subsystem interacting with a coupled environment subsystem which evolves under classical-like dynamics represented in the Wigner phase space. In studying these hybrid dynamics it becomes apparent that, for a general environment system, there exists a series of quantum correction terms that restore the hybrid equation to exact quantum dynamics. Thus it is these correction terms that influence the existence of quantum effects in the dynamics of the environment subsystem and could therefore provide unique dynamical signatures indicating the existence of quantum effects. With the above motivation, we have derived an analytical expression for the quantum propagator, including correction terms, in the case of position-dependent couplings and polynomial-potential environment systems, and we have studied, numerically, the resulting quantum dynamics in a few relevant cases through comparison of quantum-classical and quantum-corrected evolutions. The type of system chosen for numerical study consisted of a two-level, or pseudo-spin, quantum system coupled to an environment represented by a quartic potential. It was found that the Rabi oscillations of the pseudo-spin are sensitive to the quantum corrections in a certain range of parameter values, either exhibiting stronger damping or stronger oscillations, depending on the tunnelling behaviour introduced by the corrections. If one were to interpret the pseudo-spin as a Cooper-pair box and the polynomial potential as representing the oscillatory behaviour of a buckled nano-rod, then this works suggests that one might be able to witness the transition of a non-linear nano-oscillator from the realm of classical dynamics to the quantum regime by observation of the pseudo-spin Rabi oscillations. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

In this dissertation the formulation of various integration algorithms is studied, with a view to simulate quantum-classical systems in contact with a thermal bath. In particular focus is given to the constant temperature dynamics of the Nos e-Hoover, Nos e-Hoover Chain and Nos e-Hoover Power thermostat schemes. Through the use of the time symmetric Trotter factorisation of the Liouville operator, algorithms are derived that are both time-reversible and measure-preserving. The efficiency of these algorithms is tested via the constant temperature simulation of a low-dimensional harmonic system. In addition The Nos e-Hoover Power thermostat was then extended to the quantum-classical case. The damping of a tunnelling spin coupled to a thermalised harmonic mode was simulated and the results are presented. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

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