PreprintarXiv licencearXiv
Optimal Diamond Distance Estimation for Unitary Channels
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 ε, using O(√d/ε) 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).
Related
- Near-Optimal Parallel Unitary Process Tomography in Diamond Distance
- Query-optimal unitary channel tomography in diamond distance with parallel access
- Optimal classical shadow estimation of unitary channels at Heisenberg limit
- Minimal unitary representations of time-invariant causal quantum channels
- Unitary-accessible coherence-erasure distance: Exact qubit solution and a tight qutrit bound
BibTeX
@misc{bao2026optimal,
title = {{Optimal Diamond Distance Estimation for Unitary Channels}},
author = {Jinge Bao and Qisheng Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40623},
eprint = {2610.40623},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40623},
}
RIS
TY - UNPB
TI - Optimal Diamond Distance Estimation for Unitary Channels
AU - Jinge Bao
AU - Qisheng Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40623
UR - https://arxiv.org/abs/2610.40623
AB - 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 ε, using O(√d/ε) 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).
ER -