Saved in:
Bibliographic Details
Main Authors: Coladangelo, Andrea, Li, Jerry, Slote, Joseph, Wu, Ellen
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.11616
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910020013129728
author Coladangelo, Andrea
Li, Jerry
Slote, Joseph
Wu, Ellen
author_facet Coladangelo, Andrea
Li, Jerry
Slote, Joseph
Wu, Ellen
contents A central task in quantum information science is state certification: testing whether an unknown state is $ε_1$-close to a fixed target state, or $ε_2$-far. Recent work has shown that surprisingly simple measurement protocols--comprising only single-qubit measurements--suffice to certify arbitrary $n$-qubit states [Huang, Preskill, Soleimanifar '25; Gupta, He, O'Donnell '25]. However, these certification protocols are not robust: rather than allowing constant $ε_1$, they can only positively certify states within $ε_1=O(1/n)$ trace distance of the target. In many experimental settings, the appropriate error tolerance is constant as the system size grows, so this lack of robustness renders existing tests inapplicable at scale, no matter how many times the test is repeated. Here we present robust certification protocols based on few-qubit measurements that apply to all but a $O(2^{-n})$-fraction of pure target states. Our first protocol achieves constant robustness, i.e. $ε_1=Θ(1)$, using a single $O(\log n)$-qubit measurement along with single-qubit measurements in the $Z$ or $X$ basis on the other qubits. As a corollary of its robustness, this protocol also achieves constant (in $n$) copy complexity, which is optimal. Our second protocol uses exclusively single-qubit measurements and is nearly robust: $ε_1=Ω(1/\log n)$. Our tests are based on a new uncertainty principle for conditional fidelities, which may be of independent interest.
format Preprint
id arxiv_https___arxiv_org_abs_2602_11616
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Power of Two Bases: Robust and copy-optimal certification of nearly all quantum states with few-qubit measurements
Coladangelo, Andrea
Li, Jerry
Slote, Joseph
Wu, Ellen
Quantum Physics
A central task in quantum information science is state certification: testing whether an unknown state is $ε_1$-close to a fixed target state, or $ε_2$-far. Recent work has shown that surprisingly simple measurement protocols--comprising only single-qubit measurements--suffice to certify arbitrary $n$-qubit states [Huang, Preskill, Soleimanifar '25; Gupta, He, O'Donnell '25]. However, these certification protocols are not robust: rather than allowing constant $ε_1$, they can only positively certify states within $ε_1=O(1/n)$ trace distance of the target. In many experimental settings, the appropriate error tolerance is constant as the system size grows, so this lack of robustness renders existing tests inapplicable at scale, no matter how many times the test is repeated. Here we present robust certification protocols based on few-qubit measurements that apply to all but a $O(2^{-n})$-fraction of pure target states. Our first protocol achieves constant robustness, i.e. $ε_1=Θ(1)$, using a single $O(\log n)$-qubit measurement along with single-qubit measurements in the $Z$ or $X$ basis on the other qubits. As a corollary of its robustness, this protocol also achieves constant (in $n$) copy complexity, which is optimal. Our second protocol uses exclusively single-qubit measurements and is nearly robust: $ε_1=Ω(1/\log n)$. Our tests are based on a new uncertainty principle for conditional fidelities, which may be of independent interest.
title The Power of Two Bases: Robust and copy-optimal certification of nearly all quantum states with few-qubit measurements
topic Quantum Physics
url https://arxiv.org/abs/2602.11616