Conic Linear Programming in Quantum Information

A frequently studied problem in quantum resource theories (QRTs) is converting one resource state into another by applying free operations. If convexity arises in QRTs, convex analysis tools can be utilized in the analysis of these problems. The separating hyperplane theorem ensures the existence of at least one witness for each resource state in convex QRTs. By using this idea, necessary and sufficient conditions in terms of resource monotones are derived for generic convex static QRTs. We use this result to derive the complete family of conversion resource monotones for majorization as a subset of f-divergences. For classical conditional majorization, necessary and sufficient conditions for state conversion are derived in the form of a homogeneous convex function. We unified the pre-existing results under the umbrella of the resource-theoretic framework. The new approach helps in the significant simplification of the proofs. Furthermore, we extend the work to derive a new complete family of conversion monotones for quantum conditional majorization in terms of min-entropy using the same techniques and procedures. We expect the quantum conditional majorization will find operational applications in future work similar to its classical counterpart.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Mathematics & Statistics

Grantor dc:publisher.institution

Science

Year dc:date.issued

2022

Author dc:creator

• Zafar, Fasiha Binat

Advisors dc:contributor.advisor

• Gour, Gilad
• Scandolo, Carlo Maria

Committee members dc:contributor.committeemember

• Sanders, Barry C.
• Barclay, Paul

• Quantum Information
• Resource Theory
• Conic Linear Programming

Statement dc:rights

• University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

eng

DOI

http://dx.doi.org/10.11575/PRISM/39523

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/114308