Reconstructing quantum theory from diagrammatic postulates

A reconstruction of quantum theory refers to both a mathematical and conceptual paradigm that allows one derive the usual formulation from set primitive assumptions. The motivation for doing so is discomfort with theory, started its originator John von Neumann. We present finite-dimensional where all postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they category-theoretic mathematically appealing. Again equivalently, process-theoretic establishing backbone concerns manner which systems processes compose. Aside form, key novel aspect this introduction new postulate, symmetric purification. Unlike ordinary purification applies equally well classical as theory. Therefore we first reconstruct full process theoretic description consisting composite classical-quantum their interactions, before restricting ourselves just ‘fully quantum’ final step. propose two alternative manners so, ‘no-leaking’ (roughly information gain causes disturbance) ‘purity cups’ existence entangled states). Interestingly, these turn out be equivalent any cups & caps. Additionally, show how standard postulate can seen an immediate consequence purity cups. Other tangential results concern specific frameworks generalised probabilistic theories (GPTs) (a.k.a. CQM). Firstly, provide presentation GPTs, which, henceforth, subsumed under theories. Secondly, argue ‘sharp dagger’ indeed right choice dagger structure sharpness vital reconstruction.