Curator's Take
This research tackles a crucial gap between quantum theory and experimental reality by proving that quantum states can still be uniquely identified from local measurements even when those measurements contain inevitable experimental errors. The breakthrough establishes that small errors in local marginals translate to bounded errors in reconstructing the global quantum state, with the scaling relationship following a power law that varies by state type. Particularly exciting is the discovery that stabilizer states - fundamental building blocks in quantum error correction - exhibit square-root robustness, while the researchers' new classification framework could guide experimentalists toward quantum states that are more resilient to measurement noise. This work provides both theoretical foundations and practical tools like semidefinite programming methods that could significantly improve how we verify and characterize quantum states in real-world quantum computing systems.
— Mark Eatherly
Summary
A fundamental problem in quantum physics is to establish whether a multiparticle quantum state can be uniquely determined from its local marginals. In theory, this problem has been addressed in the exact case where the marginals are perfectly known. In practice, however, experiments only have access to finite statistics and therefore can only determine the marginals of a quantum state up to an error. In this Letter, we prove that unique determinability universally survives such local imperfections: specifically, for every uniquely determined state, we show that deviations of local marginals propagate to global states strictly bounded by a power law with exponent $α\in(0,1]$. This result induces a classification of multipartite quantum states by their power-law exponents, with linear scaling $α=1$ as the most favorable regime. We derive a necessary and sufficient criterion for linear robustness and translate it into an executable semidefinite-programming certification. Applying our theory, we prove that stabilizer states are inherently square-root robust and provide a complete robustness classification for the Dicke family. Finally, we exploit these results to construct a scalable two-local genuine multipartite entanglement witness, demonstrating the viability of this framework for broad practical applications.