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arXiv · 2509.12703

Sample-optimal single-copy quantum state tomography with shallow-depth measurements

Gyungmin Cho·Dohun Kim
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Abstract

Quantum state tomography (QST) is a central task in quantum information, and its efficiency is commonly characterized by sample complexity. Although collective measurements on multiple copies achieve optimal performance, they are difficult to implement on near-term devices, motivating the study of single-copy approaches. Here, we introduce an ancilla-free single-copy QST protocol based on logarithmic-depth local circuits on an $n$-qubit system. For rank-$r$ states in dimension $d=2^n$, our protocol achieves trace-norm error $\epsilon$ using $\mathcal{O}(dr^2\log d/\epsilon^2)$ copies, matching the single-copy lower bound up to a logarithmic factor. For full-rank mixed states, it removes this logarithmic overhead and achieves the optimal scaling $\mathcal{O}(d^3/\epsilon^2)$, with nearly optimal classical runtime for explicit matrix output. These results show that sample-optimal QST can be realized using experimentally accessible shallow-depth measurements.

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Gyungmin Cho, Dohun Kim. 2025-09-16. Sample-optimal single-copy quantum state tomography with shallow-depth measurements. https://arxiv.org/abs/2509.12703

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