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arXiv · 2601.04444

Nearly Time-Optimal Pure State Tomography with Pauli Measurements

Sabee Grewal·Meghal Gupta·William He·Aniruddha Sen·Mihir Singhal
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Abstract

We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\widetilde{O}(2^n/ε)$ copies of an unknown $n$-qubit pure state $|ψ\rangle$, the algorithm performs only nonadaptive Pauli measurements, runs in time $\widetilde{O}(2^n/ε)$, and outputs $|\widehatψ \rangle$ with fidelity at least $1-ε$ with $|ψ\rangle$ with high probability. This is the first algorithm for pure state tomography that achieves near-optimal running time.

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Sabee Grewal, Meghal Gupta, William He, Aniruddha Sen, Mihir Singhal. 2026-04-29. Nearly Time-Optimal Pure State Tomography with Pauli Measurements. https://arxiv.org/abs/2601.04444

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