A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
Abstract
Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via local operations with a nonvanishing probability. The classes obtained in this way are called SLOCC classes. They can be categorized into three disjoint types: the nullcone, the polystable states and strictly semistable states. Whereas the former two are well characterized, not much is known about strictly semistable states. We derive a criterion for the existence of the latter. In particular, we show that there exists a strictly semistable state if and only if there exist two polystable states whose orbits have different dimensions. We illustrate the usefulness of this criterion by applying it to tripartite states where one of the systems is a qubit. Moreover, we scrutinize all SLOCC classes of these systems and derive a complete characterization of the corresponding orbit types. We present representatives of strictly semistable classes and show to which polystable state they converge via local regular operators.
 Publication:

Quantum
 Pub Date:
 July 2020
 DOI:
 10.22331/q20200720300
 arXiv:
 arXiv:1912.00099
 Bibcode:
 2020Quant...4..300S
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 28 pages, 5 figures