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arXiv:1003.2762 · The European Physical Journal D

Entangled graphs: a classification of four-qubit entanglement

Masoud Gharahi, Seyed Javad Akhtarshenas

Published Mar 1, 2016• 23 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2016-60729-1

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Comment on “Inductive entanglement classification of four qubits under stochastic local operations and classical communication”

Masoud Gharahi, Stefano Mancini

Lamata et al. have presented an entanglement classification of four qubits under stochastic local operation and classical communication (SLOCC) based on an inductive approach [Phys. Rev. A 75, 022318 (2007)]. While it works well for three qubits, we show that some of the families for four qubits have overlaps and hence this approach is not valid for entanglement classification of four or more qubits under SLOCC.

arXiv:1811.07641•Physical Review A•Dec 20, 2018•10 citations
We propose a new classification for the entanglement in graph states based on generalized concurrence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states in 10 classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule. Furthermore, our results suggest that the generalized concurrence is a suitable measure of entanglement for multi-qubit graph states.
We propose a new classification for the entanglement in graph states based on generalized con- currence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states are in ten classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule.