Trace-invariants of colored graphs fully label LU orbits of HT multipartite states, completely characterize their LO preorder via weight-function divisibility, and yield large-N combinatorial distinctions from Haar-random states.
Partial separability revisited: Necessary and sufficient criteria
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abstract
We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial separability classes in the tripartite case contrary to a former 1+8+1. Then we give necessary and sufficient criteria for these classes, which make it possible to determine to which class a mixed state belongs. These criteria are given by convex roof extensions of functions defined on pure states. In the special case of three-qubit systems, we define a different set of such functions with the help of the Freudenthal triple system approach of three-qubit entanglement.
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2026 1verdicts
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Tensor invariants for multipartite entanglement classification
Trace-invariants of colored graphs fully label LU orbits of HT multipartite states, completely characterize their LO preorder via weight-function divisibility, and yield large-N combinatorial distinctions from Haar-random states.