1 research outputs found
Searching for extremal PPT entangled states
We study extremality in various sets of states that have positive partial
transposes. One of the tools we use for this purpose is the recently formulated
criterion allowing to judge if a given state is extremal in the set of PPT
states. First we investigate qubit--ququart states and show that the only
candidates for extremal PPT entangled states (PPTES) have ranks of the state
and its partial transposition (5,5) or (5,6) (equivalently (6,5)). Then,
examples of extremal states of (5,5) type and the so--called edge states of
type (5,6) are provided. We also make an attempt to explore the set of PPT
states with ranks (5,6). Finally, we discuss what are the possible
configurations of ranks of density matrices and their respective partial
transposition in general three-qubit and four-qubit symmetric states for which
there may exist extremal entangled PPT states. For instance in the first case
we show that the only possibilities are (4,4,4) and (4,4,5).Comment: 12 pages, 2 figures, revised version due to the partial overlap with
results of arXiv:0704.3348, some new results on extremality in multi-qubit
systems added, contribution to the special issue of Optics Communications in
memory of Krzysztof Wodkiewic