A Family of Norms With Applications In Quantum Information Theory II - Quantum PhysicsReport as inadecuate




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Abstract: We consider the problem of computing the family of operator norms recentlyintroduced in arXiv:0909.3907. We develop a family of semidefinite programsthat can be used to exactly compute them in small dimensions and bound them ingeneral. Some theoretical consequences follow from the duality theory ofsemidefinite programming, including a new constructive proof that there arenon-positive partial transpose Werner states that are r-undistillable forarbitrary r. Several examples are considered via a MATLAB implementation of thesemidefinite program, including the case of Werner states and randomlygenerated states via the Bures measure, and approximate distributions of thenorms are provided. We extend these norms to arbitrary convex mapping cones andexplore their implications with positive partial transpose states.



Author: Nathaniel Johnston, David W. Kribs

Source: https://arxiv.org/







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