A mixing time method for estimating the sample complexity of quantum state discrimination

arXiv:2609.40182 · quant-ph, cs.CC, cs.IT, math.IT, math.PR, math.RT · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.CC, cs.IT, math.IT, math.PR, math.RT

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Sample Complexity — 56× in this paper · explained in 15 episodes
• Hypergraph — 18× in this paper · explained in 2 episodes
• Fidelity — 14× in this paper · explained in 2 episodes
• Trace — 9× in this paper · explained in 2 episodes
• Trace Distance — 6× in this paper · explained in 3 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Degeneracy — 2× in this paper · explained in 3 episodes
• Stabilizer States — 2× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• No low-degree tests for quantum states
• Quantum Coupon Collector
• Optimal algorithms for learning quantum phase states
• Rounds vs Communication Tradeoffs for Maximal Independent Sets
• Optimal measurements for the dihedral hidden subgroup problem
• Quantum state discrimination
• Reversing quantum dynamics with near-optimal quantum and classical fidelity
• Operational distance and fidelity for quantum channels
• Approximate simulation of quantum channels
• General conditions for approximate quantum error correction and near-optimal recovery channels
• An invitation to the sample complexity of quantum hypothesis testing
• Quantum algorithm for a generalized hidden shift problem
• On the Duality of Teleportation and Dense Coding
• Minimax quantum state discrimination
• Optimal Detection of Symmetric Mixed Quantum States
• Complete entropic inequalities for quantum Markov chains
• Quantum Doeblin Coefficients: Interpretations and Applications
• Sample-optimal tomography of quantum states
• How many copies are needed for state discrimination?
• Contraction coefficients for noisy quantum channels

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