Category of finite-dimensional Hilbert spaces
In mathematics, the category FdHilb has all finite-dimensional Hilbert spaces for objects and the linear transformations between them as morphisms.
Properties
This category
- is monoidal,
- possesses finite biproducts, and
- is dagger compact.
According to a theorem of Selinger, the category of finite-dimensional Hilbert spaces is complete in the dagger compact category.[1][2] Many ideas from Hilbert spaces, such as the no-cloning theorem, hold in general for dagger compact categories. See that article for additional details.
References
- ^ P. Selinger, Finite dimensional Hilbert spaces are complete for dagger compact closed categories, Proceedings of the 5th International Workshop on Quantum Programming Languages, Reykjavik (2008).
- ^ M. Hasegawa, M. Hofmann and G. Plotkin, "Finite dimensional vector spaces are complete for traced symmetric monoidal categories", LNCS 4800, (2008), pp. 367–385.
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