Error message
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
Unitarity and time evolution
In functional analysis, a unitary operator is a
bounded linear operator U on a
Hilbert
space satisfying
U*U = UU* = I
where I is the identity
operator. This property is equivalent to any of the following:
- U is a surjective
isometry
- U is surjective and
preserves the inner product on the Hilbert space, so that for all
vectors x and y in the Hilbert space,
⟨Ux, Uy⟩ = ⟨x, y⟩.
Unitary matrices are precisely the unitary operators on
finite-dimensional Hilbert spaces, so the notion of a unitary operator
is a generalisation of the notion of a unitary matrix.
Unitary operators implement isomorphisms between operator
algebras.
Category:Evolutions
and Operations
Category:Handbook
of Quantum Information
Last modified:
Monday, October 26, 2015 - 17:56
