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- 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).
= Definition = In
quantum
information theory,
W-states
of n
qubits
are defined as
-
$|W\rangle = \frac{1}{\sqrt{n}}\left(|100\dots
0\rangle + |010\dots 0\rangle + \dots + |00\dots 1\rangle\right)$
Properties
One of the main properties of the
W-states
is concerned with type of
entanglement
encoding this
states.
Three qubits
Regarding to three qubits scenario: $|W\rangle = \frac{1}{\sqrt{3}}\left(|100\rangle +
|010\rangle + |001\rangle\right)$ the way of entanglement
encoding in W-states can be easy illustrated on a picture.
thumb
There is no generic three qubit entanglement in W-states and all
entanglement
monotones as well as their
normal
form will be equal to zero. However tracing out one of the parties
leaves the remaing two entangled. In this sense three qubit W-states
contain maximal amount of sum of two qubit entanglement.
Referring to the
equivalence
classes W-states define a complemetary class to the
GHZ-states.
General situation
In general case one can speak about W-type of encoding of
entanglement, which means that one deals with some
pure
state of n qubits which
contains no generic n qubit
entanglement but rather m
qubit, where m. = Physicalrealizations = W − statesareknowntorealizefirstexcitationoverthe[http : //en.wikipedia.org/wiki/Groundstategroundstate]offreespinless[http : //en.wikipedia.org/wiki/Fermionfermions]confinedtoonedimensionalchain, whicharedescribedbythefollowingHamiltioan : < math > HF = −∑iJi, i + 1ci†ci + 1.
Due to the progress made in physics of cold atoms this kind of
systems can be pretty easily produced experimentally, using for instance
trapping techniques for atoms and putting those into one dimensional
optical
lattice.
Category:Handbook
of Quantum Information
Last modified:
Monday, October 26, 2015 - 17:56
