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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Algorithms achieve near-optimal quantum state certification with limited entanglement (t=d^2 copies), plus similar results for mixedness testing and purity estimation, supported by lower bounds.
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
A concise review of sample complexities and methods for tomography and learning in continuous-variable quantum systems, with emphasis on Gaussian versus non-Gaussian states.
citing papers explorer
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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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Optimal Quantum State Testing Even with Limited Entanglement
Algorithms achieve near-optimal quantum state certification with limited entanglement (t=d^2 copies), plus similar results for mixedness testing and purity estimation, supported by lower bounds.
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Probabilistic and approximate universal quantum purification machines
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
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Advances in quantum learning theory with bosonic systems
A concise review of sample complexities and methods for tomography and learning in continuous-variable quantum systems, with emphasis on Gaussian versus non-Gaussian states.
- Quantum metrology of mixed states via purification