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We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative dagger-Frobenius monoid in the category FdHilb, which has finite-dimensional Hilbert spaces as objects and continuous linear maps as morphisms, and tensor product for the monoidal structure.
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J. Vicary (2008) Categorical formulation of C*-algebras. Proceedings of the Quantum Physics and Logic/Development of Computational Models Joint Workshop (QPL-DCM). Electronic Notes in Theoretical Computer Science, to appear
2008
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