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).
Applications of coherent classical communication and the Schur transform to quantum information theory
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory--coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half.
verdicts
UNVERDICTED 5representative citing papers
Introduces a quantum empirical operator satisfying combinatorial and large-deviation bounds to establish a quantum method of types and prove universal achievability in composite quantum hypothesis testing.
First improvement in 18 years to the depolarizing channel quantum capacity threshold via symmetry-enhanced coherent information on rank-two symmetric states.
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.
Quantum neural estimators achieve minimax-optimal copy complexity O(|Θ(U)| d / ε²) with sub-Gaussian concentration for measured Rényi relative entropies on density pairs with bounded Thompson metric.
citing papers explorer
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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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A Quantum Method of Types
Introduces a quantum empirical operator satisfying combinatorial and large-deviation bounds to establish a quantum method of types and prove universal achievability in composite quantum hypothesis testing.
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Enhanced quantum capacity thresholds from symmetry
First improvement in 18 years to the depolarizing channel quantum capacity threshold via symmetry-enhanced coherent information on rank-two symmetric states.
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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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Performance Guarantees for Quantum Neural Estimation of Entropies
Quantum neural estimators achieve minimax-optimal copy complexity O(|Θ(U)| d / ε²) with sub-Gaussian concentration for measured Rényi relative entropies on density pairs with bounded Thompson metric.