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).
- 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).
Separable and entangled states
An entangled state is defined as a state that is
not separable. A separable state can be written as a
probability distribution over uncorrelated states, product states,
ρ = ∑ipiρiA ⊗ ρiB.
Pure states
For pure states the above definition can be represented as follows.
Consider two quantum systems A
and B, with respective Hilbert
spaces ℋA and ℋB. The Hilbert space of
the composite system is the tensor product ℋA ⊗ ℋB.
If the state |Ψ⟩ABof
the composite system can be represented in the form
|Ψ⟩AB=|ψ⟩A ⊗ |ϕ⟩B,
where |ψ⟩A ∈ ℋA
and |ϕ⟩B ∈ ℋB
are the states of the systems A and B respectively, then this state is
called a separable state. If a state is not separable, it is
known as an entangled state.
Ralated papers
Category:Entanglement
Category:Handbook
of Quantum Information
Last modified:
Monday, October 26, 2015 - 17:56
