Optimal quantum channel tomography query complexity has a Heisenberg-to-classical phase transition at dilation rate τ=1: Θ(rd₁d₂/ε) on the boundary and Θ(rd₁d₂/ε²) away from it.
Online learning of quantum processes.arXiv preprint arXiv:2406.04250
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Introduces coherent swap regret against local CPTP maps and proves a three-level landscape where non-unital measurement-preparation channels force Theta(sqrt(d T log d)) minimax regret while unital channels have zero regret.
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Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition
Optimal quantum channel tomography query complexity has a Heisenberg-to-classical phase transition at dilation rate τ=1: Θ(rd₁d₂/ε) on the boundary and Θ(rd₁d₂/ε²) away from it.
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Coherent Swap Regret and Channel-Proof Learning
Introduces coherent swap regret against local CPTP maps and proves a three-level landscape where non-unital measurement-preparation channels force Theta(sqrt(d T log d)) minimax regret while unital channels have zero regret.