Information inequalities are vital to the study of both classical and quantum information theory. All of the previously known information inequalities for the von Neumann entropy can be derived from the strong subadditivity of the entropy, and one further constrained inequality. We prove the existence of an infinite family of new constrained inequalities by generalizing the proof of a family of classical information inequalities. We show that our new inequalities are all independent. We also study information inequalities for the quantum O-Renyi entropy. These are equivalent to inequalities for the ranks of marginals of multipartite quantum states. We find two new rank inequalities and provide some evidence for a third. We also find quantum states which violate a previously conjectured inequality. We then move on to study information inequalities in a physical theory which is more general than quantum mechanics: Generalized Non-Signalling Theory (GNST), which is also known as box-world. Here we find that the only information inequalities are non-negativity and subadditivity. What is surprising is that non-locality does not play a role - any bipartite entropy vector can be achieved by separable states of the theory. This is in stark contrast to the case of the von Neumann entropy in quantum theory, where only entangled states satisfy S(AB)<S(A). Finally, we study the implementation of quantum circuits via linear optics. We are able to completely characterize the set of two qubit gates which can be implemented using only linear optical elements (beam splitters and phase shifters) and post-selection. The proof also gives rise to an algorithm for calculating the optimal success probability of those gates which are achievable.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:687190 |
| Date | January 2014 |
| Creators | Cadney, Joshua |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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