Certifying bipartite entangled states with few local measurements: from separable stabilizers to applications

Abstract: We show a simple and systematic way to certify any given bipartite state as the unique joint $1$-eigenstate of two separable projectors, each of which can be measured with simple local observables. This is practically useful, as the detection probabilities of the two stabilizer projectors relate directly to the fidelity of certification. The same result gives a simple and effective lower bound on the entanglement fidelity of a quantum channel in terms of two ensemble fidelities. We then generalise the bipartite result recursively to multipartite systems, showing that every $n$-party pure state is the unique joint $1$-eigenstate of $2^{n-1}$ separable projectors, and an upper bound of the infidelity of the state in terms of the infidelities of the separable stabilizer projectors.