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).
- Deprecated function: UpdateQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: MergeQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
The trace norm ∥ρ∥1 of a matrix ρ is the sum of the singular values
of ρ. The singular values are
the roots of the eigenvalues of ρρ†.
‖ρ‖1=Tr√ρρ†.
The trace norm is the a special case p=1 of the class of
Schatten
p-norms.
Special cases
For a Hermitian matrix, like a density matrix, the absolute value of
the eigenvalues are exactly the singular values, so the trace norm is
the sum of the absolute value of the eigenvalues of the density
matrix.
Applications
The trace norm is used e.g. in the definition of the
logarithmic
negativity, which is a measure of the entanglement possed by a state
with density matrix ρ or
fidelity
between quantum states. Note that in this case one is taking the trace
norm of a partially transposed density matrix, which may have negative
eigenvalues.
Category:Mathematical
Structure
Category:Linear
Algebra
Last modified:
Monday, October 26, 2015 - 17:56
