The 14-qubit state Φ_E8 is entangled, certified by an explicit entanglement witness obtained as a rational infeasibility certificate for a semidefinite program that combines moment matrices with symmetric extension.
Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Transac- tions on Information Theory51, 2859 (2005)
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Combining moment matrices, symmetric extension, and Lov\'asz theta: $\Phi_{\text{E8}}$ is entangled
The 14-qubit state Φ_E8 is entangled, certified by an explicit entanglement witness obtained as a rational infeasibility certificate for a semidefinite program that combines moment matrices with symmetric extension.