{"paper":{"title":"Shadow Tomography of Quantum States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Scott Aaronson","submitted_at":"2017-11-03T08:07:11Z","abstract_excerpt":"We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\\rho$, as well as known two-outcome measurements $E_{1},\\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\\rho$, to within additive error $\\varepsilon$, for each of the $M$ measurements. How many copies of $\\rho$ are needed to achieve this, with high probability? Surprisingly, we give a procedure that solves the problem by measuring only $\\widetilde{O}\\left( \\varepsilon^{-4}\\cdot\\log^{4} M\\cdot\\log D\\right)$ copies. This means, for example, that we can learn the behavior of an arb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01053","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}