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
- Selinger, P. (2012) [2008]. "Finite dimensional Hilbert spaces are complete for dagger compact closed categories". Logical Methods in Computer Science. 8 (3). arXiv:1207.6972. CiteSeerX 10.1.1.749.4436. doi:10.2168/LMCS-8(3:6)2012.
- Hasegawa, M.; Hofmann, M.; Plotkin, G. (2008). "Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories". In Avron, A.; Dershowitz, N.; Rabinovich, A. (eds.). Pillars of Computer Science. Vol. 4800. Lecture Notes in Computer Science: Springer. pp. 367–385. CiteSeerX 10.1.1.443.3495. doi:10.1007/978-3-540-78127-1_20. ISBN 978-3-540-78127-1.
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