Certifying unknown-basis pure-state entanglement dimensionality with few measurement settings

arXiv:2601.11040 · quant-ph · Submitted 2026-01-16 · Read on arXiv

quant-ph

Submitted: 2026-01-16

Updated: 2026-09-23

Code: https://github.com/CYI1995/RPS

Terminology

• Entanglement — 30× in this paper · explained in 4 episodes
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Sample Complexity — 8× in this paper · explained in 15 episodes
• Fidelity — 5× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Anticoncentration — 1× in this paper · explained in 1 episode
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Shadow Tomography — 1× in this paper · explained in 4 episodes
• Steering — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Certifying entanglement dimensionality by $k$-reduction moments
• Efficient certification of high-dimensional entanglement
• Detecting high-dimensional entanglement by randomized product projections
• Certifying localizable quantum properties with constant sample complexity
• Haar random codes attain the quantum Hamming bound, approximately
• Introduction to the non-asymptotic analysis of random matrices

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