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Hilbert spaces
In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier expansion ... linear transformations such as the Fourier transform . Hilbert spaces are of crucial importance in the mathematical formulation of ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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The Church of the larger Hilbert space
... coined the phrase "Going to the Church of the Larger Hilbert Space" for the dilation constructions of channels and states , ... trace-preserving map between states on a finite-dimensional Hilbert space H . Then there exists a Hilbert space K and a unitary ...
Wiki article - Anonymous (not verified) - 05/04/2023 - 22:02 - 0 comments
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Hilbert space
REDIRECT Hilbert spaces 1249 reads Last modified: Monday, October 26, 2015 - 17:56
Wiki article - Isabeau - 26/10/2015 - 17:56 - 0 comments
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Channel (CP map)
... mapping states ( i.e. density operators) on some Hilbert space H 1 to states on some (possibly different) Hilbert space H 2 . Classical channels are included in this setup if we ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Singlet states
... theory, the representation of this group on the underlying Hilbert space can be effectively described in terms of its irreducible ... its irreducible parts will induce splitting of the whole Hilbert space into direct sum of spaces, each of them is invariant under the ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Observables and measurements
... are postulated to be Hermitian operators mapping Hilbert space H onto itself and have following properties: ... Corresponding eigenvectors or eigenstates span the Hilbert space , which means, that each observable generates an ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Bra-ket notation
... manner vectors and linear operators both in the abstract Hilbert space of the state vectors, H , and in the extensions of H ... From Riesz's representation theorem we know that a Hilbert space H and its dual space are isometrically conjugate ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Unitarity and time evolution
... operator is a bounded linear operator U on a Hilbert space satisfying U * U = U U ... U is surjective and preserves the inner product on the Hilbert space, so that for all vectors x and y in the Hilbert ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Positive operator
Definition: Given a Hilbert space H and A ∈ L (H) , A is ... x ∈ H . A positive operator on a complex Hilbert space is necessarily a symmetric operator and has a self-adjoint ... operator. The set of positive bounded operators on a Hilbert space forms a cone in the algebra of all bounded operators. ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Operators
... vectors of an abstract, separable, infinite dimensional Hilbert space H . Axiom 2: Every dynamical variable A of ... can be represented by an operator A in the Hilbert space of the vector states, in the sense that the mean values of any ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments