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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).
Monogamy is one of the most fundamental properties
of entanglement and can, in its extremal form, be expressed as follows:
If two qubits A and B are maximally quantumly correlated they cannot
be correlated at all with a third qubit C. In general, there is a
trade-off between the amount of entanglement between qubits A and B and
the same qubit A and qubit C. This is mathematically expressed by the
Coffman-Kundu-Wootters (CKW) monogamy inequality:
CAB2 + CAC2 ≤ CA(BC)2,
where CAB, CAC
are the concurrences between A and B respectively between A and C, while
CA(BC)
is the
concurrence
between subsystems A and BC.
It was proved that the above inequality can be extended to the case
of n qubits.
More generally, the monogamy inequality can be
expressed in terms of
entanglement
measures E, as
follows:
'''For any tripartite state of systems A, B1, B2 we have
E(A|B1) + E(A|B2) ≤ E(A|B1B2).'''
If the above inequality holds in general, i.e. not only for qubits, then
it can be immediately generalized by induction to the multipartite
case:
E(A|B1) + E(A|B2) + … + E(A|BN) ≤ E(A|B1B2…BN).
Notice that the
entanglement
measures EC and EF do not
satisfy the monogamy inequality, whereas
squashed-entanglement
does.
Moreover, is was proved that the
Bell-CHSH
inequality is monogamous: if three parties A, B and C share a
quantum state 𝜚 and each chooses to
measure one of two observables, then the trade-off between AB’s and AC’s
violation of the CHSH inequality is given by
|Tr(ℬCHSHAB𝜚)| + |Tr(ℬCHSHAC𝜚)| ≤ 4.
This means that if AB violate the CHSH inequality then AC cannot.
- V. Coffman
et al., Phys. Rev. A 61, 052306
(2000)
- B. M.
Terhal, Linear Algebra Appl. 323, 61
(2001)
- B.
M. Terhal, IBM J. Res. Dev. '48, 71 (2004).
Available at arXiv:quant-ph/0307120
- M. Koashi,
A. Winter, Phys. Rev. A 69, 022309
(2004)
- T. J.
Osborne, F. Verstraete, Phys. Rev. Lett. 96,
220503 (2006)
- B.
Toner, Proc. R. Soc. A 465, 59-69
(2009)
Category:Entanglement
Last modified:
Saturday, August 4, 2018 - 03:53
