Entanglement Breaking Quantum Channels, Stochastic Matrices and Primitivity

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dc.contributor.advisorKribs, David
dc.contributor.advisorPereira, Rajesh
dc.contributor.authorAhiable, Jennifer
dc.date.accessioned2021-12-22T19:15:33Z
dc.date.available2021-12-22T19:15:33Z
dc.date.copyright2021-12
dc.date.created2021-12-20
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen
dc.degree.nameMaster of Scienceen_US
dc.degree.programmeMathematics and Statisticsen_US
dc.description.abstractQuantum entanglement is a fundamental phenomenon in quantum information where states of different quantum systems are connected in a way that they cannot be described independently of each other irrespective of the spatial distance between them. We study a class of quantum channels called entanglement breaking channels. These channels break the presence of entanglement when acting on bipartite states. We also study an underlying structure describing such channels known as their Holevo form and generate stochastic matrices from them. Upon examination, we find that the nonzero spectrum and the Jordan canonical forms of such channels and their associated stochastic matrices are closely related. Focusing on conditions for primitivity of our channels, we further investigate the relationship between their primitivity indices and those of their matrices and eventually provide a quantum bound for the primitivity index of these channels. Finally, we also introduce the notion of the Holevo rank and provide a bound on these entanglement breaking channels in terms of this rank.en_US
dc.description.sponsorshipMitacs
dc.description.sponsorshipAfrican Institute for Mathematical Sciences
dc.identifier.citationAhiable, J., Kribs, D. W., Levick, J., Pereira, R., & Rahaman, M. (2021). Entanglement breaking channels, stochastic matrices, and primitivity. Linear Algebra and its Applications, 629, 219-231. https://doi.org/10.1016/j.laa.2021.08.013
dc.identifier.urihttps://hdl.handle.net/10214/26596
dc.language.isoenen_US
dc.publisherUniversity of Guelphen
dc.rights.licenseAll items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectQuantum entanglementen_US
dc.subjectEntanglement breaking channelen_US
dc.subjectCompletely positive mapen_US
dc.subjectPrimitive quantum channelen_US
dc.subjectStochastic matrixen_US
dc.subjectPrimitive matrixen_US
dc.titleEntanglement Breaking Quantum Channels, Stochastic Matrices and Primitivityen_US
dc.typeThesisen_US
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