Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum Computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities still remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focussing on deterministic computation of Boolean functions, in which natural generalisations of the Greenberger-Horne-Zeilinger (GHZ) paradox emerge; we then explore probabilistic computation, via which multipartite Bell Inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.Comment: 13 pages, 4 figures, final version accepted for publicatio

Multi-partite entanglement in quantum information processing

Quantum theories have had an unprecedented success in providing a framework for studying physical systems. A fundamental implication of these theories is the existence of so-called entangled states, that is states whose description cannot be reduced to their constituents. These states are purely quantum and there is no such analogue in classical physics, where knowing the state of every particle is sufficient to infer the state of the system they compose. Entanglement is a core element of many quantum algorithms, quantum teleportation, quantum communications and quantum cryptographic scenarios. Furthermore, entanglement is present in nearly all solid-state systems, when they are at, or close to, their state of lowest energy. Therefore, it is both a technological resource and also a property which needs to be investigated in order to achieve understanding of real world materials at a fundamental level. The most concise demonstration of entanglement is perhaps in the case of maximal entanglement between two spin-l/2 particles. These maximally entangled two- particle states are called Bell states and they have been used to demonstrate experimentally that quantum mechanics is inequivalent to classical mechanics. A gen- eralization of this setting comes from studying entanglement between two physical systems, these can be either pure or mixed (e.g. in contact with a thermal bath). Entanglement between two systems, also knows as bipartite entanglement, has been studied in depth and quantified through various measures. However bipartite entanglement, by definition, is not the only quantity of in- terest. In some cases, entanglement is global and its properties cannot be reduced to studying bi-partitions. This type of entanglement, so-called multipartite entanglement, is harder to quantify and to study in general. Its presence is profound in physical systems that are at the point of undergoing a quantum phase transition and it is also a core ingredient for quantum error correcting codes, performing classical computation with quantum resources and some cryptographic scenarios. In this thesis we study properties of systems with multi-partite entanglement in the context of renormalization and quantum phase transitions, we show that multi- partite entanglement can be used to perform cryptographic tasks and we investigate what classes of Hamiltonians generate multiartite entanglement, while at the same time, their action can be simulated efficiently by a classical computer.EThOS - Electronic Theses Online ServiceGBUnited Kingdo