Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.687190
Title: Information inequalities and quantum circuits
Author: Cadney, Joshua
ISNI:       0000 0004 5922 6186
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2014
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Abstract:
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)
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.687190  DOI: Not available
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