An exponential query advantage from access to Stinespring dilation unitaries in quantum channel learning

arXiv:2609.40001 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Fidelity — 21× in this paper · explained in 2 episodes
• Query Complexity — 17× in this paper · explained in 2 episodes
• Accuracy — 15× in this paper · explained in 1 episode
• Trace — 10× in this paper · explained in 2 episodes
• Entanglement — 9× in this paper · explained in 3 episodes
• Hilbert Space — 8× in this paper · explained in 2 episodes
• Trace Distance — 4× in this paper · explained in 3 episodes
• Benchmarking — 3× in this paper · explained in 3 episodes
• Process tomography — 3× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Ambient Dimension — 1× in this paper · explained in 1 episode
• Block Encoding — 1× in this paper · explained in 4 episodes
• Fingerprinting — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• A Survey of Quantum Property Testing
• Quantum tomography using state-preparation unitaries
• Quantum Algorithms for Estimating Physical Quantities using Block-Encodings
• The power of oracle access: Optimal sample and query complexity of the abelian state hidden subgroup problem
• Distributional property testing in a quantum world
• Measuring Less to Learn More: Quadratic Speedup in learning Nonlinear Properties of Quantum Density Matrices
• New Quantum Algorithms for Computing Quantum Entropies and Distances
• A Quantum Algorithm Framework for Discrete Probability Distributions with Applications to R'enyi Entropy Estimation
• Fast Quantum Algorithms for Trace Distance Estimation
• Quantum algorithms for Uhlmann transformation
• No Universal Purification in Quantum Mechanics
• Conjugate queries can help
• Local Test for Unitarily Invariant Properties of Bipartite Quantum States
• Random Stinespring superchannel: converting channel queries into dilation isometry queries
• Random dilation superchannel
• Quantum channel tomography and estimation by local test
• General teleportation channel, singlet fraction and quasi-distillation
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Robust randomized benchmarking of quantum processes
• Recovering quantum gates from few average gate fidelities

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