1Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland
2Institute for Theoretical Physics, University of Innsbruck, A–6020 Innsbruck, Austria
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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 non-vanishing probability. The classes obtained in this way are called SLOCC classes. They can be categorized into three disjoint types: the null-cone, 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.
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Cited by
[1] Adam Burchardt and Zahra Raissi, “Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States”, arXiv:2003.13639.
[2] Antoine Neven, David Gunn, Martin Hebenstreit, and Barbara Kraus, “Local Transformations of Multiple Multipartite States”, arXiv:2007.06256.
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Source: https://quantum-journal.org/papers/q-2020-07-20-300/
