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Finite-dimensional Quantum Observables are the Special Symmetric Dagger-Frobenius Algebras of CP Maps

Published 13 Oct 2021 in quant-ph | (2110.07074v3)

Abstract: We use purity, a principle borrowed from the foundations of quantum information, to show that all special symmetric dagger-Frobenius algebras in CPM(fHilb) are canonical, i.e. that they arise by doubling of special symmetric dagger-Frobenius algebras in fHilb. In particular, this applies to all classical structures.

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