Abstract

While there is no doubt about the success of Quantum Mechanics in explaining - beautifully - many of the problems concerning different physical topics, it is nowadays still an open theory with several challenges which compels both Physics and Mathematics. Just a few years ago, it was a common believe that the big unsolved problems pertained to the domain of Quantum Gravitation Theory, the conjunction of Quantum Field Theory and General Relativity. Quantum Gravity, String Theory and Grand Unification Theories (GUTS) are closely related to unsolved challenges of modern mathematics concerning algebraic topology and algebraic geometry. However, to the surprise of many, the emerging field of Quantum Information Theory has shown that even in the non-relativistic quantum theory there exist still fundamental open problems. The characterization of entanglement, separability and distillability are among these, and again they are linked to mathematical unsolved challenges in C*-algebras, linear algebra and geometry functional analysis.

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