Instance-optimal high-precision shadow tomography with few-copy measurements

Sisi Zhou derives instance-optimal sample-complexity bounds for high-precision shadow tomography using measurements on one or a few copies at a time. For a given observable set, an optimisation formula involving the inverse Fisher-information matrix characterises the necessary and sufficient number of copies up to a logarithmic factor. The result links quantum learning and quantum metrology and includes adaptive measurements and potentially dimension-dependent precision thresholds.