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This is a database of entanglement in graph states of up to 12 qubits, the result of a joint work by A. Cabello, L.E. Danielsen, A.J. López-Tarrida, and J.R. Portillo. For more details, see the paper [4]. Entanglement in graph states has previously been classified for states of up to 7 qubits [1], and for 8 qubits [2].

We also list cardinality-multiplicity invariants that distinguish graph states. (Note that for 9 or more qubits, there is a small number of pairs of exceptional states that are not distinguished [4].) Cardinality-multiplicity invariants were first defined and calculated for up to 8 qubits in [3].


File format

The file format is as follows. See [4] for more detailed definitions. Each line gives data about one graph state, and has the following format:



n Download Size
2 entanglement2 1 graph
3 entanglement3 1 graph
4 entanglement4 2 graphs
5 entanglement5 4 graphs
6 entanglement6 11 graphs
7 entanglement7 26 graphs
8 entanglement8 101 graphs
9 entanglement9 440 graphs
10 entanglement10 3132 graphs (509 KB)
11 entanglement11.bz2 40,457 graphs (1.2 MB compressed)
12 entanglement12.bz2 1,274,068 graphs (45 MB compressed)

We have also written a computer program that, given a graph, finds optimal representatives in the LC orbit (in terms of number of edges and chromatic index) and gives LC-sequence(s) producing the input graph from the optimal graph(s):

findoptimal.cC source code



[1] M. Hein, J. Eisert, and H.J. Briegel. "Multiparty entanglement in graph states." Phys. Rev. A 69, 062311 (2004)

[2] A. Cabello, A.J. López-Tarrida, P. Moreno, and J.R. Portillo. "Entanglement in eight-qubit graph states." Phys. Lett. A 373, 2219-2225 (2009)

[3] A. Cabello, A.J. López-Tarrida, P. Moreno, and J.R. Portillo. "Compact set of invariants characterizing graph states of up to eight qubits." Phys. Rev. A 80, 012102 (2009)

[4] Adán Cabello, Lars Eirik Danielsen, Antonio J. López-Tarrida, and José R. Portillo. Optimal preparation of graph states. Nov. 2010. (Submitted for publication) (arXiv)