Local operations assisted by classical communication (LOCC) constitute thefree operations in entanglement theory. Hence, the determination of LOCCtransformations is crucial for the understanding of entanglement. Wecharacterize here almost all LOCC transformations among pure states of $n>3$$d$--level systems with $d>2$. Combined with the analogous results for$n$-qubit states shown in G. Gour, B. Kraus, N. R. Wallach, J. Math. Phys. 58,092204 (2017) this gives a characterization of almost all local transformationsamong multipartite pure states. We show that non-trivial LOCC transformationsamong generic fully entangled pure states are almost never possible. Thus,almost all multipartite states are isolated. They can neither bedeterministically obtained from local unitary (LU)-inequivalent states vialocal operations, nor can they be deterministically transformed to pure fullyentangled LU-inequivalent states. In order to derive this result we prove amore general statement, namely that generically a state possesses nonon-trivial local symmetry. We show that these results also hold for certaintripartite systems.
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机译：纠缠理论中的经典操作（LOCC）辅助了本地操作。因此，确定LOCC变换对于理解纠缠至关重要。我们在这里表征$ n> 3 $$ d $的纯状态之间的几乎所有LOCC转换-$ d> 2 $的级别系统。结合G.Gour，B.Kraus，N.R.Wallach，J.Math。物理58,092204（2017）给出了多部分纯状态中几乎所有局部转换的特征。我们表明，在泛型完全纠缠的纯态之间进行非平凡的LOCC转换几乎是不可能的。因此，几乎所有的多部分状态都是孤立的。它们既不能通过局部运算从局部unit（LU）不等价状态确定地获得，也不能确定性地转换为纯完全纠缠的LU不等价状态。为了得出这个结果，我们证明了一个更笼统的说法，即一个国家一般具有非平凡的局部对称性。我们证明这些结果也适用于某些三方系统。
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