Research establishes limits on the samples needed to estimate quantum mutual information, highlighting implications for spacetime models.
Key Points
This research aims to determine the fundamental limits on the number of samples required to accurately estimate quantum mutual information for pure bipartite states.
Utilized Schmidt decomposition to relate quantum mutual information to local von Neumann entropy.
Leveraged Wang's established lower bound for entropy estimation to derive sample complexity results.
Derived rigorous sample scaling as Ω~(d2/ϵ) for estimating I(A:B) with prescribed accuracy ϵ.
The number of samples required for estimating I(A:B) scales as Ω~(d2/ϵ), indicating significant growth with dimension and accuracy.
The findings indicate that stability is required in emergent spacetime models to apply sample complexity results directly.