TWO NOVEL APPROACHES IN QUANTUM ENTANGLEMENT THEORY

Abstract

Quantum entanglement is a phenomenon popularised for its intriguing, counter-intuitive character. This thesis aims to introduce two novel approaches to the theory of quantum entanglement— absolutely entangled sets of states, and dynamics-based entanglement witnesses. Entanglement as a notion relies on specifying the partition of the Hilbert space into subsystems. Absolutely entangled sets of states are sets of quantum states that feature entanglement under any global basis change. We formalise this notion for bipartitions and multipartitions, providing first results in this direction. With recent advances in optomechanics where entanglement is probed at the mesoscopic and macroscopic scales, entanglement witnesses that make minimal assumptions on the system are desired. A dynamics-based entanglement witness is semi-device-independent in that, it only assumes knowledge of the dynamics of the system. We consider harmonic dynamics, and present a first result in witnessing entanglement of coupled harmonic oscillators, that builds on Tsirelon's test for nonclassicality.