= Local-energy measurement verification
Uniformly sample one positive local term and measure the effect $h_j$. The averaged energy-flag effect on a witness is $H/M$, where $M$ is the number of terms. Repetition with a threshold halfway between the promised flag probabilities uses $O(M^2/(b-a)^2)$ witness registers for constant error. A spectral tensor-product analysis, as in <QMA parallel repetition with entangled witnesses>, proves soundness against entangled witnesses. Constant-locality <positive operator-valued measures> are efficiently implementable using one <ancilla qubit>.
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