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A note on tomography of states with low stabilizer rank
Abstract
In this note, we consider tomography of n-qubit quantum states |ψ⟩ that are promised to have stabilizer rank k i.e., admit a stabilizer decomposition of |ψ⟩ = ∑i=1k ci |ϕi⟩ where each |ϕi⟩ is a stabilizer state. We give a tomography protocol for such states up to trace distance ε > 0 running in textsfpoly(n,2k,1/ε) time and thus can handle k=O(log n) efficiently. This follows from first showing that the stabilizer extent ξ(|ψ⟩), which is the minimal ℓ1 norm over the coefficients {ci} of any stabilizer decomposition of |ψ⟩, can be bounded as ξ(|ψ⟩) ≤ 2O(k) and improving upon the previous best bound of kO(k). The protocol is then obtained by utilizing a tomography protocol for states with bounded stabilizer extent.
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BibTeX
@misc{dutt2026note,
title = {{A note on tomography of states with low stabilizer rank}},
author = {Arkopal Dutt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03658},
eprint = {2610.03658},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03658},
}
RIS
TY - UNPB
TI - A note on tomography of states with low stabilizer rank
AU - Arkopal Dutt
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03658
UR - https://arxiv.org/abs/2610.03658
AB - In this note, we consider tomography of n-qubit quantum states |ψ⟩ that are promised to have stabilizer rank k i.e., admit a stabilizer decomposition of |ψ⟩ = ∑_i=1^k c_i |ϕ_i⟩ where each |ϕ_i⟩ is a stabilizer state. We give a tomography protocol for such states up to trace distance ε > 0 running in textsfpoly(n,2^k,1/ε) time and thus can handle k=O(log n) efficiently. This follows from first showing that the stabilizer extent ξ(|ψ⟩), which is the minimal ℓ_1 norm over the coefficients {c_i} of any stabilizer decomposition of |ψ⟩, can be bounded as ξ(|ψ⟩) ≤ 2^O(k) and improving upon the previous best bound of k^O(k). The protocol is then obtained by utilizing a tomography protocol for states with bounded stabilizer extent.
ER -