Conic Linear Programming in Quantum Information
Date
2022-01
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Abstract
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.
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Keywords
Quantum Information, Resource Theory, Conic Linear Programming
Citation
Zafar, F. B. (2022). Conic linear programming in quantum information (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.