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APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory

The 2016 APS Medal for Excellence in Physics was given to Edward Witten. This contribution was invited in conjunction with this award. These original notes contain concise explanations of some key results in the axiomatic and algebraic approaches to quantum field theory, which are relevant to quantum entanglement. They serve to put the connection between quantum field theory and quantum information theory on a precise and rigorous footing.