Pauli Measurements Are Near-Optimal for Pure State Tomography

• URL: http://arxiv.org/abs/2601.04444v1
• Date: Wed, 07 Jan 2026 23:16:37 GMT
• Title: Pauli Measurements Are Near-Optimal for Pure State Tomography
• Authors: Sabee Grewal, Meghal Gupta, William He, Aniruddha Sen, Mihir Singhal,
• Abstract summary: We give an algorithm for pure state tomography with near-optimal copy complexity using single-qubit measurements.<n>Specifically, given $widetildeO (2n/)$ copies of an unknown pure $n$-qubit state $lvertrangle$, the algorithm performs only textitnonadaptive Pauli measurements.
• Score: 2.207442386128469
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give an algorithm for pure state tomography with near-optimal copy complexity using single-qubit measurements. Specifically, given $\widetilde{O}(2^n/ε)$ copies of an unknown pure $n$-qubit state $\lvertψ\rangle$, the algorithm performs only \textit{nonadaptive Pauli measurements}, runs in time $\mathrm{poly}(2^n,1/ε)$, and outputs $\lvert \widehatψ \rangle$ that has fidelity $1-ε$ with $\lvert ψ\rangle$ with high probability. This improves upon the previous best copy complexity bound of $\widetilde{O}(3^n/ε)$.

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