Optimal Quantum Algorithm for Estimating Fidelity to a Pure State

Fuente: arXiv
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Main Authors: Fang, Wang, Wang, Qisheng
Format: Preprint
Published: 2025
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author Fang, Wang
Wang, Qisheng
author_facet Fang, Wang
Wang, Qisheng
contents We present an optimal quantum algorithm for fidelity estimation between two quantum states when one of them is pure. In particular, the (square root) fidelity of a mixed state to a pure state can be estimated to within additive error $\varepsilon$ by using $Θ(1/\varepsilon)$ queries to their state-preparation circuits, achieving a quadratic speedup over the folklore $O(1/\varepsilon^2)$. Our approach is technically simple, and can moreover estimate the quantity $\sqrt{\operatorname{tr}(ρσ^2)}$ that is not common in the literature. To the best of our knowledge, this is the first query-optimal approach to fidelity estimation involving mixed states.
format Preprint
id arxiv_https___arxiv_org_abs_2506_23650
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal Quantum Algorithm for Estimating Fidelity to a Pure State
Fang, Wang
Wang, Qisheng
Quantum Physics
Information Theory
We present an optimal quantum algorithm for fidelity estimation between two quantum states when one of them is pure. In particular, the (square root) fidelity of a mixed state to a pure state can be estimated to within additive error $\varepsilon$ by using $Θ(1/\varepsilon)$ queries to their state-preparation circuits, achieving a quadratic speedup over the folklore $O(1/\varepsilon^2)$. Our approach is technically simple, and can moreover estimate the quantity $\sqrt{\operatorname{tr}(ρσ^2)}$ that is not common in the literature. To the best of our knowledge, this is the first query-optimal approach to fidelity estimation involving mixed states.
title Optimal Quantum Algorithm for Estimating Fidelity to a Pure State
topic Quantum Physics
Information Theory
url https://arxiv.org/abs/2506.23650