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.

This category theory-related article is a stub. You can help Wikipedia by .

[1] 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).

[2] M. Hasegawa, M. Hofmann and G. Plotkin, "Finite dimensional vector spaces are complete for traced symmetric monoidal categories", LNCS 4800, (2008), pp. 367–385.

[1]

[2]