Breaking the Multiplicative Overhead in Quantum Entropy Estimation

arXiv:2609.40179 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Accuracy — 29× in this paper · explained in 1 episode
• Calibration — 21× in this paper · explained in 7 episodes
• Trace — 12× in this paper · explained in 2 episodes
• Query Complexity — 8× in this paper · explained in 2 episodes
• Entanglement — 7× in this paper · explained in 3 episodes
• Block Encoding — 5× in this paper · explained in 4 episodes
• SIGACT Symposium on Theory of Computing — 4× in this paper
• Sample Complexity — 3× in this paper · explained in 15 episodes
• Algorithmic Primitives — 2× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Ambient Dimension — 1× in this paper · explained in 1 episode
• Chebyshev Polynomials — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• A List of Complexity Bounds for Property Testing by Quantum Sample-to-Query Lifting
• A Lower Bound Framework for Quantum Functional Estimation
• Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions
• On the Second-Order Asymptotics of the Partially Smoothed Conditional Min-Entropy & Application to Quantum Compression
• Information-Theoretic Lower Bounds for Approximating Monomials via Optimal Quantum Tsallis Entropy Estimation
• Conjugate queries can help
• Near optimal quantum algorithm for estimating Shannon entropy
• Near-Optimal Simultaneous Estimation of Quantum State Moments
• Sublinear quantum algorithms for estimating von Neumann entropy
• Towards Minimax Estimation of High-Order Functionals by Quantum Arguments
• Trace Estimation of Quantum State Powers: Sample Complexity and Computational Hardness
• Optimal von Neumann Entropy Estimation
• Local and Global Risk Bounds for Quantum Entropy Estimation under Projective-Design Measurements
• On Estimating the Quantum Tsallis Relative Entropy

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