Research map / Learning theory and algorithms / Sample complexity
Purest Quantum State Identification
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Introduces purest quantum state identification (PQSI) as a best-arm-identification-style problem and gives incoherent (IM-PQSI) and coherent SWAP-test (CM-PQSI) successive-rejects algorithms plus a fixed-two-outcome-POVM lower bound, with no experiments.
Problem
Identifying the purest (least noisy) quantum state among K unknown n-qubit states using N copies, where the learner must also choose measurement bases under single-copy or multi-copy access.
Approach
Casts purest-state identification as a best-arm identification problem where each state's purity is estimated via Haar-random measurement collision statistics (incoherent) or SWAP-test outcomes (coherent), with successive rejection allocating more copies to surviving candidates; a lower bound is obtained by reducing to purest random-state identification with Haar-random two-outcome POVMs.
Key results
- Incoherent IM-PQSI achieves error probability exp(-Omega(N H_1/(log(K) 2^n))) under a purity-gap assumption Delta >= c > 1/d^2.
- Coherent CM-PQSI via SWAP test achieves error bound exp(-N H_2/(8 log(K))) with H_2 = min Delta^2/i, showing separation from incoherent strategies.
- Lower bound: any fixed two-outcome incoherent POVM strategy has error at least exp(-O(N H_1/2^n)).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use coherent (two-copy) measurement with the SWAP test instead of incoherent single-copy measurement | PQSI · PQSI | error probability: e_N \leq \frac{K(K-1)}{2}\exp\left(- \frac{N H_2}{8\overline{\log}(K) } \right) | Helped |
Limitations
- Incoherent lower bound only covers fixed two-outcome random POVMs, not all POVMs.
- Incoherent upper bound requires purity gaps at least 1/d^2 (assumption), otherwise a weaker bound with m=d applies.
- No experimental validation reported.
Experimental setup
Metrics: error probability
Builds on: best arm identification successive rejects unitary designs
Closest papers by meaning
- Online Learning of Pure States is as Hard as Mixed States (NeurIPS 2025 · similarity 0.88)
- SSL4Q: Semi-Supervised Learning of Quantum Data with Application to Quantum State Classification (ICML 2024 · similarity 0.86)
- Toward the Goldilocks Blind Compression of Quantum States (NeurIPS 2026 · similarity 0.86)
- Limitations of measure-first protocols in quantum machine learning (ICML 2025 · similarity 0.85)
- Reinforced Learning Explicit Circuit Representations for Quantum State Characterization from Local Measurements (ICML 2025 · similarity 0.85)
- One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective (NeurIPS 2026 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.