Finite-Size Limits of Adaptive Pauli Prediction

Abstract:Can quantum data reliably answer questions chosen from earlier results? We prove that $M$ adaptive Pauli predictions on $n$ qubits require $\Omega(\sqrt{\min\{n,M\}})$ copies at fixed accuracy. Published upper bounds make this tight for $M\le n$. Thus $n$ adaptive predictions cost $\Theta(\sqrt n)$ copies, whereas a fixed list costs only $O(\log n)$. The lower bound uses diagonal states and commuting observables, identifying a statistical cost of adaptation. We also quantify how this cost increases with precision.

arXiv:2610.13652 [quant-ph]

(or arXiv:2610.13652v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.13652 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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