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Quantum state certification

arXiv 1708.06002 ↗First posted 20 Aug 2017quant-ph cs.DScited by 13

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Abstract (arXiv)

We consider the problem of quantum state certification, where one is given n copies of an unknown d-dimensional quantum mixed state ρ, and one wants to test whether ρ is equal to some known mixed state σ or else is ε-far from σ. The goal is to use notably fewer copies than the Omega(d2) needed for full tomography on ρ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using n = O(d/ε) copies, and one with respect to trace distance using n = O(d/ε2) copies. The latter algorithm also applies when σ is unknown as well. These copy complexities are optimal up to constant factors.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Aug 2017.

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Citing papers per year: 2021: 2; 2022: 2; 2023: 0; 2024: 4; 2025: 4; 2026: 1.

13 papers.

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  1. 2021Exponential separations between learning with and without quantum memorycited by 50
  2. 2021Toward Instance-Optimal State Certification With Incoherent Measurementscited by 12
  3. 2022When Does Adaptivity Help for Quantum State Learning?cited by 12
  4. 2022Tight Bounds for Quantum State Certification with Incoherent Measurementscited by 11
  5. 2024Certifying almost all quantum states with few single-qubit measurementscited by 7
  6. 2024Stabilizer bootstrapping: A recipe for efficient agnostic tomography and magic estimationcited by 5
  7. 2024On the sample complexity of purity and inner product estimationcited by 4
  8. 2025Estimating quantum relative entropies on quantum computerscited by 2
  9. 2025Sampling and Identity-Testing Without Approximate Tensorization of Entropycited by 1
  10. 2025Instance-Optimal Quantum State Certification with Entangled Measurementscited by 1
  11. 2026Multi-Armed Sequential Hypothesis Testing by Bettingcited by 1
  12. 2024New Bounds on Quantum Sample Complexity of Measurement Classescited by 0
1 more
  1. 2025Non-iid hypothesis testing: from classical to quantumcited by 0