Certifying bipartite entangled states with few local measurements: from separable stabilizers to applications
Jennifer Ahiable, Andreas Winter
TL;DR
This work introduces a measurement-efficient framework for certifying pure entangled states under local operations by characterizing any bipartite target state as the unique +1 eigenstate of two separable projectors P and Q, yielding a robust fidelity bound F(ρ,ψ)^2 ≥ Tr(ρP) + Tr(ρQ) − 1 and an LOCC-implementable certification scheme. It further shows a channel-entanglement fidelity bound in terms of ensemble fidelities, and extends the idea recursively to multipartite systems, constructing a cascade of 2^{n−1} separable projectors whose product stabilizes the target state and provides a scalable fidelity guarantee. The method offers a practical, experiment-friendly route to certify complex entangled states using only local measurements, with explicit bounds on infidelity and a clear LOCC protocol, while also outlining open questions about scaling and applicability. Overall, it provides a principled, structure-driven alternative to general tomography for fidelity estimation of pure states and their induced channels.
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.