The work proves a worst-case sample complexity of O(sqrt(4.5^n)) for distributed inner product estimation with local Clifford sampling on n-qubit states, with a conjectured O(sqrt(3.6^n)) for Haar sampling.
In particular, the underlying fourth-moment com- parison is already not saturated forn=1 andn=2
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Worst-Case Sample Complexity Bounds for Distributed Inner Product Estimation with Local Randomized Measurements
The work proves a worst-case sample complexity of O(sqrt(4.5^n)) for distributed inner product estimation with local Clifford sampling on n-qubit states, with a conjectured O(sqrt(3.6^n)) for Haar sampling.