Relations between bipartite entanglement measures
(pp0085-0113)
Katharina
Schwaiger and Barbara Kraus
doi:https://doi.org/10.26421/QIC18.1-2-5
Abstracts:
We investigate the entanglement of bipartite systems from
an operational point of view. Main emphasis is put on bipartite pure
states in the single copy regime. First, we present an operational
characterization of bipartite pure state entanglement, viewing the state
as a multipartite state. Then, we investigate the properties and
relations of two classes of operational bipartite and multipartite
entanglement measures, the so-called source and the accessible
entanglement. The former measures how easy it is to generate a given
state via local operations and classical communication (LOCC) from some
other state, whereas the latter measures the potentiality of a state to
be convertible to other states via LOCC. We investigate which parameter
regime is physically available, i.e. for which values of these measures
does there exist a bipartite pure state. Moreover, we determine, given
some state, which parameter regime can be accessed by it and from which
parameter regime it can be accessed. We show that this regime can be
determined analytically using the Positivstellensatz. We compute the
boundaries of these sets and the boundaries of the corresponding source
and accessible sets. Furthermore, we relate these results to other
entanglement measures and compare their behaviors.
Key words:
Pure bipartite entanglement, Positivstellensatz |