The logarithmic negativity is an entanglement measure which is easily computable and an upper bound to the
distillable entanglement.[4]
It is defined as
where is the partial transpose operation and denotes the
trace norm.
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:
is not asymptotically continuous. That means that for a sequence of
bipartite Hilbert spaces (typically with increasing dimension) we can have a sequence of quantum states which converges to (typically with increasing ) in the
trace distance, but the sequence does not converge to .
is an upper bound to the distillable entanglement
References
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