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- 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).
The negativityquant-ph/0102117 is an
entanglement
measure which is easy to compute.
The negativity can be defined as:
$$\mathcal{N}(\rho) :=
\frac{||\rho^{\Gamma_A}||_1-1}{2}$$
where:
- ρΓA
is the
partial
transpose of ρ with
respect to subsystem A
- $||X||_1 = Tr|X| = Tr \sqrt{X^\dagger
X}$ is the
trace
norm or the sum of the sigular values of the operator X.
An alternative and equivalent definition is the absolute sum of the
negative eigenvalues of ρΓA:
$$\mathcal{N}(\rho) := \sum_i
\frac{|\lambda_{i}|-\lambda_{i}}{2}$$ where λi are all of
the eigenvalues.
Properties
𝒩(∑ipiρi) ≤ ∑ipi𝒩(ρi)
𝒩(P(ρi)) ≤ 𝒩(ρi)
-
where P(ρ) is an
arbitrary
LOCC
operation over ρ
See also
Category:Quantum
Information Theory
Category:Handbook
of Quantum Information
Category:Entanglement
Last modified:
Monday, October 26, 2015 - 17:56
