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).
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.
Optimal query algorithms for testing unitary channels under depolarizing noise yield Θ(1/ε) complexity with matching lower bounds even for adaptive ancilla-assisted protocols.
The paper shows that for some pairs of unitary channels, perfect discrimination is possible with separable states but nearly impossible with maximally entangled states, introducing MEWC and MEBC concepts.
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.
citing papers explorer
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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
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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Unitary Channel Testing Under a Depolarizing Noise Assumption
Optimal query algorithms for testing unitary channels under depolarizing noise yield Θ(1/ε) complexity with matching lower bounds even for adaptive ancilla-assisted protocols.
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Entanglement in quantum channel discrimination: sometimes less is more
The paper shows that for some pairs of unitary channels, perfect discrimination is possible with separable states but nearly impossible with maximally entangled states, introducing MEWC and MEBC concepts.
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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.