Full Multipartite Entanglement of Frequency-Comb Gaussian States

An analysis is conducted of the multipartite entanglement for Gaussian states generated by the parametric down-conversion of a femtosecond frequency comb. Using a recently introduced method for constructing optimal entanglement criteria, a family of tests is formulated for mode decompositions that extends beyond the traditional bipartition analyses. A numerical optimization over this family is performed to achieve maximal significance of entanglement verification. For experimentally prepared 4-, 6-, and 10-mode states, full entanglement is certified for all of the 14, 202, and 115 974 possible nontrivial partitions, respectively.

Figure 1

Structure of 4-mode state. The spectral components (top panel) and partitionings (bottom panel) are shown.

Figure 2

Significance of all partitions for the 6-mode states where the partitions are ordered according to the significance of the detected entanglement. All of the values are negative except for a single positive value, which represents the trivial partition, $K=1$, and cannot be entangled.

Figure 3

The verified entanglement for all 115 974 nontrivial partitions—sorted by significance $\mathrm{\Sigma }$—for the 10-mode frequency-comb Gaussian state.