Abstract
Quantum mechanics has a history more than 100 years, and there are still many challenging open-ended questions. The problems encountered in modern physics such as matrix mechanics and quantum information often involve both quantum theory and open-ended problems in modern mathematics such as linear algebra. Distillability problem is an important open-ended problem in the field of quantum information and linear algebra. This article recalls the development history and application of linear algebra, summarizes the background and progress of distillability conjecture, and attempts to explore this problem by summarizing and using the knowledge of linear algebra and matrix theory learned in the course.
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