Quantum channel tomography query complexity transitions from Heisenberg scaling Θ(r d1 d2 / ε) at dilation rate τ=1 to classical scaling Θ(r d1 d2 / ε²) for τ ≥ 1+Ω(1).
Optimal lower bound for quantum channel tomography in away-from-boundary regime.arXiv preprint arXiv:2601.10683
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Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition
Quantum channel tomography query complexity transitions from Heisenberg scaling Θ(r d1 d2 / ε) at dilation rate τ=1 to classical scaling Θ(r d1 d2 / ε²) for τ ≥ 1+Ω(1).