Near-optimal incoherent tomography of low-rank quantum channels
Abstract
We study tomography for quantum channels with input dimension d1, output dimension d2, and Kraus rank at most r, to within diamond norm error ε, using adaptive experiments that retain no quantum memory between channel queries. - For quantum channels whose non-zero Choi eigenvalues are bounded below by Ω(d1/r), we establish optimal query upper and lower bounds Θ(d1d2r2/ε2). The upper bound is achieved by a nonadaptive algorithm that uses the estimator from [Surawy-Stepney et al., Quantum (2022)], together with a new diamond-norm analysis. The lower bound applies to arbitrary adaptive incoherent protocols and follows from a new local family of channels and a uniform one-query Fisher-information bound. - For general channels, we establish an upper bound O(d1d2r2log(2d1)/ε2), nearly matching the above lower bound Ω(d1d2r2/ε2). To achieve this, we generalize the above nonadaptive algorithm by adapting the input state over O(log(2d1)) rounds with the Matrix Multiplicative Weight Update algorithm.
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BibTeX
@misc{chen2026nearoptimal,
title = {{Near-optimal incoherent tomography of low-rank quantum channels}},
author = {Kean Chen and Aadil Oufkir},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23752},
eprint = {2609.23752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23752},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Near-optimal incoherent tomography of low-rank quantum channels
AU - Kean Chen
AU - Aadil Oufkir
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23752
UR - https://arxiv.org/abs/2609.23752
AB - We study tomography for quantum channels with input dimension d_1, output dimension d_2, and Kraus rank at most r, to within diamond norm error ε, using adaptive experiments that retain no quantum memory between channel queries. - For quantum channels whose non-zero Choi eigenvalues are bounded below by Ω(d_1/r), we establish optimal query upper and lower bounds Θ(d_1d_2r^2/ε^2). The upper bound is achieved by a nonadaptive algorithm that uses the estimator from [Surawy-Stepney et al., Quantum (2022)], together with a new diamond-norm analysis. The lower bound applies to arbitrary adaptive incoherent protocols and follows from a new local family of channels and a uniform one-query Fisher-information bound. - For general channels, we establish an upper bound O(d_1d_2r^2log(2d_1)/ε^2), nearly matching the above lower bound Ω(d_1d_2r^2/ε^2). To achieve this, we generalize the above nonadaptive algorithm by adapting the input state over O(log(2d_1)) rounds with the Matrix Multiplicative Weight Update algorithm.
ER -