Relativistic entanglement of single and two particle systems

One of the defining features of quantum theory is entanglement, the notion that quantum systems can display correlations that are impossible from the classical
point of view. In quantum information theory entanglement has come to be recognised as a physical resource that enables new technologies that perform information
processing tasks which are beyond the limits of the classical realm. It has been realised only recently that entanglement is dependent on the frame of reference in
both inertial and accelerated systems. In this thesis, we investigate the relativistic entanglement of massive spin-1=2 particles in inertial frames by focussing on the
dependence of entanglement on the geometry of the underlying boost scenario. We first explore the ‘qubit’ of the relativistic setting: a single particle with spin and momentum, with momentum given by a Gaussian distribution. We study the system in a variety of different boost scenarios, analysing the behaviour of entanglement
from a geometric point of view. The spin-spin entanglement of two particle systems is then surveyed for many different discrete product and entangled momenta, with the spins in the Werner state. We also extend the analysis to continuous momentum states and study them in a variety of geometries. The results obtained from the analysis of discrete states are applied to continuous states, leading to a better
understanding of the behaviour of entanglement. We lastly discuss the common view according to which Lorentz boosts leave the total entanglement of the state invariant.