Finite-Sample Selected Covariance Spectra in Classical Shadows

arXiv:2606.00527 · quant-ph · Submitted 2026-05-30 · Read on arXiv

quant-ph

Submitted: 2026-05-30

Updated: 2026-09-22

Comments: The title and the presentation were improved. The technical contents were not changed

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 9× in this paper · explained in 1 episode
• Ambient Dimension — 7× in this paper · explained in 1 episode
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Shadow Tomography — 3× in this paper · explained in 4 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Post-Selection — 2× in this paper · explained in 2 episodes
• Sample Complexity — 2× in this paper · explained in 15 episodes
• Core — 1× in this paper · explained in 2 episodes
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Reconstruction Error — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• A useful variant of the Davis--Kahan theorem for statisticians
• The randomized measurement toolbox
• Shadow tomography on general measurement frames
• Shadow Tomography Against Adversaries
• Classical shadows with arbitrary group representations
• Training variational quantum circuits with CoVaR: covariance root finding with classical shadows

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