Entanglement Structure Certification Based on Energy-Restricted State Discrimination

The certification of entanglement in multipartite scenarios is crucial for the advancement of quantum technologies, particularly for the realization of large-scale quantum networks. Here, we introduce a method to certify the structure of the entanglement in ensembles of quantum states with limited energy based on a state discrimination game played by multiple distant and uncharacterized parties. The optimal success probability of this game forms a strict hierarchy, determined by the number of bipartitions and the size of the entangled subsets in each state of the underlying ensemble. The game can be optimally won using a single, fixed measurement setting shared by all parties, regardless of the specific entanglement structure. We further demonstrate that both the performance and noise robustness of our method improve in the multipartite regime, scaling exponentially with the number of parties. Consequently, our approach enables the exclusion of entire structural classes, thereby certifying the structure of multipartite entanglement.

💡 Research Summary

The paper introduces a semi‑device‑independent protocol for certifying the structure of multipartite entanglement using an energy‑restricted state discrimination game. A preparation device receives classical bits (x₀, x₁, …) and, subject to a global energy bound ⟨H⟩≤ω, encodes them into quantum states that are distributed to n distant parties. Each party performs the same fixed local measurement and aims to recover its own input bit. The figure of merit is the average success probability pₛ that all parties correctly guess their bits.

First, the authors prove that shared randomness does not enlarge the set of achievable success probabilities: any strategy involving a random variable λ can be simulated by a deterministic pure‑state preparation together with a fixed measurement. This closure property allows the optimisation to be carried out over pure states only.

For separable (product) strategies, the problem reduces to two independent single‑party discrimination tasks. Each party’s success probability is bounded by the function W₂(ω_A) (or W₂(ω_B)), which is the optimal discrimination probability for a two‑state ensemble under an energy constraint ω_A (or ω_B). The global energy constraint translates into (1−ω_A)(1−ω_B)≥1−ω. Solving the resulting constrained optimisation yields an explicit expression for the maximal separable success probability

p_sep = ¼