Two computable sets of multipartite entanglement measures
Beatrix C. Hiesmayr, Marcus Huber, Philipp Krammer · Physical Review A · 2009
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called ``separability'' measure, reveals which of the subsystems are separable or entangled. For that we have to extend the concept of $k$ separability for multipartite systems to a unambiguous separability concept which we call ${\ensuremath{\gamma}}_{k}$ separability. The second set of entanglement measures reveals the ``kind'' of entanglement, i.e., if it is bipartite, tripartite, \dots{}, $n$-partite entangled and is denoted as the ``physical'' measure. We show how lower bounds on both sets of measures can be obtained by the observation that any entropy may be rewritten via operational expressions known as $m$ concurrences. Moreover, for different classes of bipartite or multipartite qudit systems we compute the bounds explicitly and discover that they are often tight or equivalent to positive partial transposition.