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.
Quantum channel testing in average-case distance
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Introduces the random Stinespring superchannel to convert channel queries into isometry queries, yielding a channel analogue of Uhlmann's theorem and proving optimal channel learning query complexity of Θ(d_A d_B r).
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).
A randomized algorithm detects dissipation of magnitude at least epsilon in unknown Lindbladian dynamics with optimal total evolution time O(epsilon^{-1}) under bounded strength and locality assumptions.
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Strict Hierarchy for Quantum Channel Certification to Unitary
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.
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Random Stinespring superchannel: converting channel queries into dilation isometry queries
Introduces the random Stinespring superchannel to convert channel queries into isometry queries, yielding a channel analogue of Uhlmann's theorem and proving optimal channel learning query complexity of Θ(d_A d_B r).
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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).
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Optimal detection of dissipation in Lindbladian dynamics
A randomized algorithm detects dissipation of magnitude at least epsilon in unknown Lindbladian dynamics with optimal total evolution time O(epsilon^{-1}) under bounded strength and locality assumptions.