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- 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).
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- 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).
- Deprecated function: SelectQueryInterface::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
Entanglement of formation
The entanglement of formation is an
entanglement
measure for
bipartite
quantum states.
It is defined as
Ef(ρ) = minℰpiEE(|ψi⟩)
where the minimization is over all
ensembles
of pure states ℰ = {(pi, |ψi⟩)}
that realizes the given state, ρ = ∑ipi|ψi⟩⟨ψi|,
and EE(|ψ⟩)
is the
entropy
of entanglement which is defined for pure states. This kind of
extension of a quantity defined on pure states to mixed states is called
a
convex
roof construction.
Entanglement of formation quantifies how many
bell
states are needed per copy of to prepare many copies of ρ using the following specific
LOCC
procedure:
- For each copy, select which pure state |ϕi⟩ to prepare
from a probability distribution qi.
- For each of the different |ϕi⟩, prepare
the required number of copies from bell states.
- Discard the information about which copy is in which pure
state.
Until recently, it was not known if entanglement of formation was
equal to the
entanglement
cost. It was shown in 2008 that the quantities are not equal, and
furthermore that entanglement of formation is not additive (see
section
XIV D). However, the entanglement cost is equal to the
regularization of the entanglement of formation,
Ec(ρ)=lim
Category:Entanglement
Category:Mathematical
structure
Last modified:
Wednesday, March 1, 2017 - 07:35
