Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.
Local test for unitarily invariant properties of bipartite quantum states
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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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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.