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Partition GHZ SLOCC class of three qubits into ten families under LU · arXivDesk

2201.07377Jan 19, 20229 pages, no figures. Delete the motivation in previous version. Change abstract, introduction, main text, summary and references

Partition GHZ SLOCC class of three qubits into ten families under LU

Dafa Li

Quantum Physics

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Abstract

In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.

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