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Category of finite-dimensional Hilbert spaces

Index 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. [1]

9 relations: Biproduct, Category (mathematics), Dagger compact category, Hilbert space, Linear map, Mathematics, Monoidal category, Morphism, No-cloning theorem.

Biproduct

In category theory and its applications to mathematics, a biproduct of a finite collection of objects, in a category with zero objects, is both a product and a coproduct.

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Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.

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Dagger compact category

In mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Doplicher and Roberts on the reconstruction of compact topological groups from their category of finite-dimensional continuous unitary representations (that is, Tannakian categories).

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Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Monoidal category

In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.

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Morphism

In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.

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No-cloning theorem

In physics, the no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state.

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Redirects here:

Category of finite dimensional Hilbert spaces, Category of finite dimensional hilbert spaces, FdHilb, Fdhilb, Finite dimensional Hilbert spaces, Finite dimensional hilbert spaces.

References

[1] https://en.wikipedia.org/wiki/Category_of_finite-dimensional_Hilbert_spaces

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