means that the quantum state of a particle ensemble cannot be described under the assumption that particles interacted with each other only in groups having fewer than
It has been used to characterize the quantum states created in experiments with cold gases.
Entanglement depth appeared in the context of spin squeezing.
[1] Later it was formalized in terms of convex sets of quantum states, independent of spin squeezing as follows.
-producible mixed states form a convex set.
A quantum state contains at least multiparticle entanglement of
-entanglement is called genuine multipartite entangled.
Finally, a quantum state has an entanglement depth
Since there is not a general method to detect multipartite entanglement, these methods had to be tailored to experiments with various relevant quantum states.
Thus, entanglement criteria has been developed to detect entanglement close to symmetric Dicke states with
[3][4][5] They are very different from spin-squeezed states, since they do not have a large spin polarization.
They can provide Heisenberg limited metrology, while they are more robust to particle loss than Greenberger-Horne-Zeilinger (GHZ) states.
There are also criteria for detecting the entanglement depth in planar-squeezed states.
[6] Planar squeezed states are quantum states that can be used to estimate a rotation angle that is not expected to be small.
[7] Finally, multipartite entanglement can be detected based on the metrological usefulness of the quantum state.
[8][9] The criteria applied are based on bounds on the quantum Fisher information.
[1] has been used in many experiments with cold gases in spin-squeezed states.
[10][11][12][13][14] There have also been experiments in cold gases for detecting multipartite entanglement in symmetric Dicke states.
[4][15] There have been also experiments with Dicke states that detected entanglement based on metrological usefulness in cold gases[16] and in photons.