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  "path": "/abs/2606.26034v1",
  "publishedAt": "2026-06-25T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Qisheng Wang"
  ],
  "textContent": "**Authors:** Qisheng Wang\n\nWe consider the problem of estimating the fidelity of an unknown quantum state to a known reference state to within additive error $\\varepsilon$. We show that the sample complexity is $O(r^2/\\varepsilon^2)$ with optimal $\\varepsilon$-dependence when the reference state is of rank $r$, improving the previous best $O(r^2\\log^2(1/\\varepsilon)/\\varepsilon^4)$ due to Utsumi, Nakata, Wang, and Takagi (QIP 2026). We also provide a lower bound of $Ω(r/\\varepsilon^2)$, improving the previous best $Ω(r/\\varepsilon+1/\\varepsilon^2)$, with implications to quantum query complexity. Moreover, we further consider the case where the unknown state is of rank at most $r$ while the reference state can be arbitrary, for which the sample complexity is shown to be $O(r^2/\\varepsilon^4)$. As an application, we present an approach to tolerant quantum state certification, generalizing the exact certification studied in Bădescu, O'Donnell, and Wright (STOC 2019).",
  "title": "Estimating Fidelity to a Reference Quantum State"
}