Coherent quantum inference achieves O(1/ε) sample complexity for d-dimensional quantum purity amplification, exponentially better than the Ω(d/ε) required by any incoherent measurement-mediated protocol.
Random purification channel made simple.Preprint arXiv:2511.23451, 2025
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For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
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 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.
Presents a poly-complexity quantum circuit implementing the random dilation superchannel for parallel channel queries, with approximate sequential extension, a no-go theorem for exact sequential dilation, and an application to exponentially improved channel storage-retrieval.
New purification-based reformulations of QCRB and HCRB connect mixed-state metrology bounds to those of purified states, enabling asymptotic attainment of HCRB or 2×QCRB via random channels and individual measurements.
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.
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An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
Coherent quantum inference achieves O(1/ε) sample complexity for d-dimensional quantum purity amplification, exponentially better than the Ω(d/ε) required by any incoherent measurement-mediated protocol.
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Cloning is as Hard as Learning for Stabilizer States
For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
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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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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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Random dilation superchannel
Presents a poly-complexity quantum circuit implementing the random dilation superchannel for parallel channel queries, with approximate sequential extension, a no-go theorem for exact sequential dilation, and an application to exponentially improved channel storage-retrieval.
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Quantum metrology of mixed states via purification
New purification-based reformulations of QCRB and HCRB connect mixed-state metrology bounds to those of purified states, enabling asymptotic attainment of HCRB or 2×QCRB via random channels and individual measurements.
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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.