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dc.contributor.authorJaques, Samuel
dc.contributor.authorRahaman, Mizanur 15:33:59 (GMT) 15:33:59 (GMT)
dc.descriptionThe final publication is available at Elsevier via © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.description.abstractWe investigate spectral properties of the tensor products of two completely positive and trace preserving linear maps (also known as quantum channels) acting on matrix algebras. This leads to an important question of when an arbitrary subalgebra can split into the tensor product of two subalgebras. We show that for two unital quantum channels the multiplicative domain of their tensor product splits into the tensor product of the individual multiplicative domains. Consequently, we fully describe the fixed points and peripheral eigen operators of the tensor product of channels. Through a structure theorem of maximal unital proper *-subalgebras (MUPSA) of a matrix algebra we provide a non-trivial upper bound of the recently-introduced multiplicative index of a unital channel. This bound gives a criteria on when a channel cannot be factored into a product of two different channels. We construct examples of channels which cannot be realized as a tensor product of two channels in any way. With these techniques and results, we found some applications in quantum information theory.en
dc.description.sponsorshipNSERC Discovery Grant University of Regina Graduate Student Research Fellowship NSERC Canadian Graduate Scholarship Department of Combinatorics and Optimization, University of Waterloo Post-Doctoral Fellowship of the Department of Pure Mathematics, University of Waterlooen
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.subjectFixed pointsen
dc.subjectMultiplicative domainen
dc.subjectQuantum channelen
dc.subjectSpectral propertyen
dc.subjectTensor producten
dc.titleSpectral properties of tensor products of channelsen
dcterms.bibliographicCitationElsevierJaques, S., & Rahaman, M. (2018). Spectral properties of tensor products of channels. Journal of Mathematical Analysis and Applications, 465(2), 1134–1158.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen
uws.contributor.affiliation2Pure Mathematicsen

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