All k-qubit reduced density matrices of an n-qubit state can be reconstructed from e^{O(k)} log^2(n) rounds of parallel product measurements using perfect hash families.
Scaling the ion trap quantum processor
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Quantum Overlapping Tomography
All k-qubit reduced density matrices of an n-qubit state can be reconstructed from e^{O(k)} log^2(n) rounds of parallel product measurements using perfect hash families.