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Title: Quantum Sizes: Complexity, Dimension and Many-Box Locality
Authors: CAI YU
Keywords: quantum, complexity, nonlocality
Issue Date: 18-Aug-2015
Citation: CAI YU (2015-08-18). Quantum Sizes: Complexity, Dimension and Many-Box Locality. ScholarBank@NUS Repository.
Abstract: Quantum physics is probably the most successful and fascinating physical theory of the last century. Alongside with its success, quantum mechanics has some features that are less intuitive to our classical mind. This thesis examines some of these features with the concept of "size" measures: tree size complexity, dimension and many-box locality; and studies how these sizes elucidate the quantum{classical boundary. Tree size (TS) complexity is a complexity measure of quantum states proposed by Aaronson. A (family of) state is complex if its tree size scales superpolynomial in the number of qubits. By studying a mathematical theorem that puts superpolynomial lower bound on tree size, we exhibit explicit examples of complex states, and efficient witnessing of them. Moreover, the relation between tree size complexity and quantum computation is discussed. Dimension witnesses (DW) are tests that allow one to certify the lower bound of the dimension, the number of perfectly distinguishable states of the physical system. By violating a device independent dimension witness, one can certify the presence of states of high dimension. We discuss a device independent dimension witness for entangled four dimensional systems (ququarts) based on the CGLMP4 inequality. We propose the notion of many-box locality (MBL) as a possible physical principle that defines the quantum set of correlations. Novel tools are developed to analyse MBLN, the sets of correlations that become local when N copies are measure together. The set MBL8 matches the quantum set on a slice of the two-party, two-input, two-outcome no-signalling polytope.
Appears in Collections:Ph.D Theses (Open)

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