Characterising Quantum Phenomena

: Entanglement, Channels and Measurement

Abstract

Quantum information is a critical resource in many new, emerging technologies. However, challenges remain in characterising entanglement in quantum states and the full characterisation of quantum channels. In addition, key aspects of quantum phenomena, such as measurement and the quantum-to-classical transition are not yet fully understood. In this thesis, we present new techniques that advance the characterisation of quantum states and channels. In addition, we explore how measurement results can emerge from unitary dynamics, using the framework of quantum Darwinism and states of spectrum broadcast structure. We present a steering protocol that uses semidefinite programming to find optimal steering inequalities, certifying qubit entanglement without requiring full-state tomography. Applying entanglement certification to high-dimensional quantum channels, we then adapt a steering and entanglement witness to certify the dimensionality of a quantum channel with varying levels of trust. Additionally, we propose a technique for correcting the effects of finite statistics in a quantum steering experiment, which can lead to false positive outcomes in any test for entanglement. Finally, we shift perspective and explore the more fundamental question of modelling quantum measurements from a dynamical lens. We consider measurement itself to be an entropy-increasing unitary process, driven by the second law of thermodynamics. In this paradigm, measurement outcomes emerge objectively from unitary dynamics via closed-system equilibration. We derive an error bound that quantifies the probability an observer will obtain an incorrect measurement outcome and develop numerical techniques using a random matrix model to investigate the conditions under which the measurement error is minimal.

Date of Award	4 Feb 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Mehul Malik (Supervisor), Sabine Wollmann (Supervisor) & John G Rarity (Supervisor)