dc.contributor.advisor	Benerjee, Subhahsish
dc.creator.researcher	Dutta, Supriyo
dc.date.accessioned	2023-12-06T10:42:04Z
dc.date.available	2023-12-06T10:42:04Z
dc.date.awarded	2019-01
dc.date.issued	2018-01
dc.date.registered	2014
dc.description.abstract	My doctoral research is at the interface of quantum information and graph theory. A Laplacian of a graph is a positive semidefinite, Hermitian matrix. A quantum state is represented by a density matrix that is a positive semidefinite Hermitian matrix with unit trace. Therefore, corresponding to every graph G there is a quantum state which is represented by the density matrix, (G) = 1 trace(K(G)) K(G); where K(G) is the combinatorial or signless Laplacian matrix of G. Here, we call these quantum states as graph Laplacian quantum states. Analogous to classical computation, in quantum computation, we utilise quantum gates, for instance, the Pauli X; Y;Z, Hadamard, and CNOT gates. A graph theoretic counterpart of these operations is modelled by the graph-theoretic technique, called graph switching. We have developed a combinatorial procedure for each of these quantum gates. As a result, it is possible to generate a graph theoretical construction of Bell states, widely used in quantum information theory. Detection of entanglement in a quantum state is one of the fundamental problems in quantum mechanics. Partial transpose is a crucial tool in entanglement detection. We have constructed a graph theoretical counterpart of this tool and used it to detect entanglement in higher dimensional quantum states. A number of graph isomorphisms can be utilised in generating entanglement from mixed separable states of arbitrary dimensions. Apart from quantum entanglement, another well-known class of quantum correlations is quantum discord, which is also used as a resource, in quantum information processing. We have demonstrated graph theoretical criterion for non-zero discord in quantum states. On the basis of these conditions, we have provided a graph theoretic measure of quantum discord applicable for graph Laplacian quantum states. We have generalized some of these results for weighted digraphs. My doctoral work is bidirectional. It attempts a connection between graph theory and quantum mechanics. Graph theoretic partial transpose is a valuable contribution of this effort. Constructing non-isomorphic cospectral graphs is one of the oldest challenging problems, in spectral graph theory. Using partial transpose we may construct a number of varieties of these graphs. The broad theme of my work is to develop and exploit the connections between quantum mechanics and graph theory in such a way that both these, hitherto distinct fields behave in a symbiotic manner.	en_US
dc.description.note	col. ill.; including bibliography	en_US
dc.description.statementofresponsibility	by Supriyo Dutta	en_US
dc.format.accompanyingmaterial	CD	en_US
dc.format.extent	xix, 97p.	en_US
dc.identifier.accession	TP00031
dc.identifier.citation	Dutta, Supriyo. (2019). Graph Theoretic Aspects of Quantum Information Processing (Doctor's thesis). Indian Institute of Technology Jodhpur, Jodhpur.	en_US
dc.identifier.uri	https://ir.iitj.ac.in/handle/123456789/41
dc.language.iso	en
dc.publisher	Indian Institute of Technology Jodhpur
dc.publisher.department	Mathematics	en_US
dc.publisher.place	Jodhpur
dc.rights.holder	IIT Jodhpur
dc.rights.license	CC-BY-NC-SA
dc.subject.ddc	Graph	en_US
dc.subject.ddc	Theoretic Aspects	en_US
dc.subject.ddc	Quantum	en_US
dc.subject.ddc	Information	en_US
dc.subject.ddc	Processing	en_US
dc.title	Graph Theoretic Aspects of Quantum Information Processing	en_US
dc.type	Thesis

Graph Theoretic Aspects of Quantum Information Processing

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