Positively factorizable maps
نویسندگان
چکیده
We initiate a study of linear maps on Mn(C) that have the property they factor through tracial von Neumann algebra (A,τ) via operators Z∈Mn(A) whose entries consist positive elements from von-Neumann algebra. These often arise in context non-local games especially synchronous case. establish connection with convex sets Rn containing self-dual cones and existence these maps. The Choi matrix map this kind which an abelian turns out to be completely (CP) matrix. fully characterize positively factorizable rank is 2. also provide some applications analysis finding doubly nonnegative matrices are not CPSD. A special class examples found concept Unextendible Product Bases quantum information theory.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2021
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2021.09.003