Optimal Diamond Distance Estimation for Unitary Channels

The diamond distance between two quantum channels determines the optimal probability of distinguishing them from a single use. We give a quantum algorithm that estimates the diamond distance between two unknown $d$-dimensional unitary channels to within additive error $\varepsilon$, using $O(\sqrt{d}/\varepsilon)$ queries to the unitary channels and their inverses. The query complexity is optimal, as it matches the lower bound due to Jeon and Oh (npj Quantum Inf. 2026).

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40623
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

Optimal Diamond Distance Estimation for Unitary Channels

Jinge Bao, Qisheng Wang
arXiv (Cornell University)
Quantum Computing Algorithms and Architecture
preprint

Optimal Diamond Distance Estimation for Unitary Channels

Jinge Bao, Qisheng Wang
preprint en

Abstract

The diamond distance between two quantum channels determines the optimal probability of distinguishing them from a single use. We give a quantum algorithm that estimates the diamond distance between two unknown $d$-dimensional unitary channels to within additive error $\varepsilon$, using $O(\sqrt{d}/\varepsilon)$ queries to the unitary channels and their inverses. The query complexity is optimal, as it matches the lower bound due to Jeon and Oh (npj Quantum Inf. 2026).

arXiv (Cornell University)
Quantum Computing Algorithms and Architecture
DOIOpen Access PDFOpenAlex
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Optimal Diamond Distance Estimation for Unitary Channels — Jinge Bao, Qisheng Wang · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS