The category of operator spaces and complete contractions is locally countably presentable, yields intuitionistic and classical linear logic models, and its Chu-construction duality reproduces the Heisenberg-Schrödinger duality of quantum theory.
American Mathematical Society, 1997
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Operator Spaces, Linear Logic and the Heisenberg-Schr\"odinger Duality of Quantum Theory
The category of operator spaces and complete contractions is locally countably presentable, yields intuitionistic and classical linear logic models, and its Chu-construction duality reproduces the Heisenberg-Schrödinger duality of quantum theory.