Fig. 1. Conceptual scheme.

Alice (A) and Bob (B) initially share an unknown input state ∣Ψ_i⟩. To certify entanglement of the state, they locally perform a set of weak measurements ${\mathcal{M}}_{\{p_A,{\overrightarrow{r}}_A\}}^{(A)}$ and ${\mathcal{M}}_{\{p_B,{\overrightarrow{r}}_B\}}^{(B)}$, where the measurement strength p and direction $\overrightarrow{r}$ can be adjusted. In this process, they obtain measurement outcomes (±1 for each), which are used for entanglement certification tests (3, 4, and 5); as the measurement back action, the input state changes to another pure state ∣Ψ_m⟩, which still contains some entanglement. After passing the certification tests, the original entanglement is fully recovered by reversal measurements ${\mathcal{R}}_{\{q_A,{\overrightarrow{s}}_A\}}^{(A)}$ and ${\mathcal{R}}_{\{q_B,{\overrightarrow{s}}_B\}}^{(B)}$, which succeeds probabilistically. As a result of these consecutive measurements, the final state becomes the original entangled state, ∣Ψ_f⟩ = ∣Ψ_i⟩, and thus, it can be further harnessed for quantum technologies.