It relates to the negativity quant-ph/0102117 as follows:
EN(ρ) : = log2(2N + 1).
The logarithmic negativity
- can be zero even if the state is entangled (if the state is PPT entangled)
- does not reduce to the entropy of entanglement on pure states like most other entanglement measures
- is additive on tensor products: EN(ρ ⊗ σ) = EN(ρ) ⋅ EN(σ)
- is not asymptotically continuous. That means that for a sequence of bipartite Hilbert spaces H1, H2, … (typically with increasing dimension) we can have a sequence of quantum states ρ1, ρ2, … which converges to ρ ⊗ n1, ρ ⊗ n2, … (typically with increasing ni) in the trace distance, but the sequence EN(ρ1)/n1, EN(ρ2)/n2, … does not converge to EN(ρ).
- is an upper bound to the distillable entanglement
Monday, October 26, 2015 - 17:56