Optimal spectrum estimation

arXiv:2609.30171 · quant-ph, cs.CC, cs.DS · Submitted 2026-09-24 · Read on arXiv

quant-ph, cs.CC, cs.DS

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Trace — 22× in this paper · explained in 2 episodes
• Accuracy — 19× in this paper · explained in 1 episode
• Chebyshev Polynomials — 13× in this paper · explained in 2 episodes
• Sample Complexity — 6× in this paper · explained in 15 episodes
• Adaptivity — 3× in this paper · explained in 1 episode
• Approximation Bound — 3× in this paper · explained in 1 episode
• Entanglement — 3× in this paper · explained in 3 episodes
• Fidelity — 3× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• Measuring Quantum Entropy
• Spectrum estimation of density operators with alkaline-earth atoms
• Orbital entanglement in bond-formation processes
• When Does Adaptivity Help for Quantum State Learning?
• Non-iid hypothesis testing: from classical to quantum
• Spectrum Estimation is Almost as Hard as Tomography
• Quantum U-statistics
• Improved Quantum Algorithms for Fidelity Estimation
• Optimal von Neumann Entropy Estimation
• Sample-optimal tomography of quantum states
• Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance
• Quantum universal variable-length source coding
• Fidelity Estimation to a Known Quantum State Is Nearly Quadratic in the Smaller Rank
• Random dimension reduction and learning symmetric properties of quantum states
• Sharper Bounds for Chebyshev Moment Matching, with Applications
• Efficient quantum tomography
• Quantum Spectrum Testing
• The Keyl-Werner algorithm is not optimal for spectrum estimation
• Quantum algorithms for Uhlmann transformation
• A Lower Bound Framework for Quantum Functional Estimation

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity